diff --git a/doc/Textbooks/.DS_Store b/doc/Textbooks/.DS_Store
index 3a6051c5d..75c5352a2 100644
Binary files a/doc/Textbooks/.DS_Store and b/doc/Textbooks/.DS_Store differ
diff --git a/doc/pub/week35/html/._week35-bs010.html b/doc/pub/week35/html/._week35-bs010.html
index 182f6bb0f..24461334b 100644
--- a/doc/pub/week35/html/._week35-bs010.html
+++ b/doc/pub/week35/html/._week35-bs010.html
@@ -379,14 +379,14 @@ $$
 \alpha = \boldsymbol{z}^T\boldsymbol{x},
 $$
 
-<p>which means that (using our previous example) we have</p>
+<p>which means that (using our previous example and keeping track of our definition of the derivative of a scalar) we have</p>
 $$
-\frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}=\boldsymbol{A}^T\boldsymbol{y}.
+\frac{\partial \alpha}{\partial \boldsymbol{x}} = \frac{\partial \boldsymbol{z}^T\boldsymbol{x}}{\partial \boldsymbol{x}}=\boldsymbol{z}^T=\boldsymbol{A}^T\boldsymbol{y}.
 $$
 
 <p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one is just the transpose of the other.</p>
 
-<p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
+<p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
 $$
 \frac{\partial \alpha}{\partial \boldsymbol{y}} = \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T.
 $$
diff --git a/doc/pub/week35/html/._week35-bs014.html b/doc/pub/week35/html/._week35-bs014.html
index 3e251c1f6..9ebd409ce 100644
--- a/doc/pub/week35/html/._week35-bs014.html
+++ b/doc/pub/week35/html/._week35-bs014.html
@@ -364,9 +364,14 @@ MathJax.Hub.Config({
 
 <p>We list here some other useful relations we may encounter (recall that vectors are defined by boldfaced low-key letters)</p>
 $$
-\frac{\partial (\boldsymbol{b}^T\boldsymbol{a})}{\partial \boldsymbol{a}} = \boldsymbol{b},
+\frac{\partial (\boldsymbol{x}^T\boldsymbol{a})}{\partial \boldsymbol{x}} = \boldsymbol{a}^T,
 $$
 
+$$
+\frac{\partial (\boldsymbol{a}^T\boldsymbol{x})}{\partial \boldsymbol{x}} = \boldsymbol{a}^T,
+$$
+
+
 $$
 \frac{\partial tr(\boldsymbol{B}\boldsymbol{A})}{\partial \boldsymbol{A}} = \boldsymbol{B}^T,
 $$
diff --git a/doc/pub/week35/html/week35-reveal.html b/doc/pub/week35/html/week35-reveal.html
index fb3474d30..78deaf60f 100644
--- a/doc/pub/week35/html/week35-reveal.html
+++ b/doc/pub/week35/html/week35-reveal.html
@@ -537,16 +537,16 @@ $$
 $$
 <p>&nbsp;<br>
 
-<p>which means that (using our previous example) we have</p>
+<p>which means that (using our previous example and keeping track of our definition of the derivative of a scalar) we have</p>
 <p>&nbsp;<br>
 $$
-\frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}=\boldsymbol{A}^T\boldsymbol{y}.
+\frac{\partial \alpha}{\partial \boldsymbol{x}} = \frac{\partial \boldsymbol{z}^T\boldsymbol{x}}{\partial \boldsymbol{x}}=\boldsymbol{z}^T=\boldsymbol{A}^T\boldsymbol{y}.
 $$
 <p>&nbsp;<br>
 
 <p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one is just the transpose of the other.</p>
 
-<p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
+<p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
 <p>&nbsp;<br>
 $$
 \frac{\partial \alpha}{\partial \boldsymbol{y}} = \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T.
@@ -715,7 +715,13 @@ $$
 <p>We list here some other useful relations we may encounter (recall that vectors are defined by boldfaced low-key letters)</p>
 <p>&nbsp;<br>
 $$
-\frac{\partial (\boldsymbol{b}^T\boldsymbol{a})}{\partial \boldsymbol{a}} = \boldsymbol{b},
+\frac{\partial (\boldsymbol{x}^T\boldsymbol{a})}{\partial \boldsymbol{x}} = \boldsymbol{a}^T,
+$$
+<p>&nbsp;<br>
+
+<p>&nbsp;<br>
+$$
+\frac{\partial (\boldsymbol{a}^T\boldsymbol{x})}{\partial \boldsymbol{x}} = \boldsymbol{a}^T,
 $$
 <p>&nbsp;<br>
 
diff --git a/doc/pub/week35/html/week35-solarized.html b/doc/pub/week35/html/week35-solarized.html
index eabfc92d3..9310fb771 100644
--- a/doc/pub/week35/html/week35-solarized.html
+++ b/doc/pub/week35/html/week35-solarized.html
@@ -602,14 +602,14 @@ $$
 \alpha = \boldsymbol{z}^T\boldsymbol{x},
 $$
 
-<p>which means that (using our previous example) we have</p>
+<p>which means that (using our previous example and keeping track of our definition of the derivative of a scalar) we have</p>
 $$
-\frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}=\boldsymbol{A}^T\boldsymbol{y}.
+\frac{\partial \alpha}{\partial \boldsymbol{x}} = \frac{\partial \boldsymbol{z}^T\boldsymbol{x}}{\partial \boldsymbol{x}}=\boldsymbol{z}^T=\boldsymbol{A}^T\boldsymbol{y}.
 $$
 
 <p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one is just the transpose of the other.</p>
 
-<p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
+<p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
 $$
 \frac{\partial \alpha}{\partial \boldsymbol{y}} = \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T.
 $$
@@ -739,9 +739,14 @@ $$
 
 <p>We list here some other useful relations we may encounter (recall that vectors are defined by boldfaced low-key letters)</p>
 $$
-\frac{\partial (\boldsymbol{b}^T\boldsymbol{a})}{\partial \boldsymbol{a}} = \boldsymbol{b},
+\frac{\partial (\boldsymbol{x}^T\boldsymbol{a})}{\partial \boldsymbol{x}} = \boldsymbol{a}^T,
 $$
 
+$$
+\frac{\partial (\boldsymbol{a}^T\boldsymbol{x})}{\partial \boldsymbol{x}} = \boldsymbol{a}^T,
+$$
+
+
 $$
 \frac{\partial tr(\boldsymbol{B}\boldsymbol{A})}{\partial \boldsymbol{A}} = \boldsymbol{B}^T,
 $$
diff --git a/doc/pub/week35/html/week35.html b/doc/pub/week35/html/week35.html
index ce93085af..64d36e6e1 100644
--- a/doc/pub/week35/html/week35.html
+++ b/doc/pub/week35/html/week35.html
@@ -679,14 +679,14 @@ $$
 \alpha = \boldsymbol{z}^T\boldsymbol{x},
 $$
 
-<p>which means that (using our previous example) we have</p>
+<p>which means that (using our previous example and keeping track of our definition of the derivative of a scalar) we have</p>
 $$
-\frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}=\boldsymbol{A}^T\boldsymbol{y}.
+\frac{\partial \alpha}{\partial \boldsymbol{x}} = \frac{\partial \boldsymbol{z}^T\boldsymbol{x}}{\partial \boldsymbol{x}}=\boldsymbol{z}^T=\boldsymbol{A}^T\boldsymbol{y}.
 $$
 
 <p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one is just the transpose of the other.</p>
 
-<p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
+<p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
 $$
 \frac{\partial \alpha}{\partial \boldsymbol{y}} = \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T.
 $$
@@ -816,9 +816,14 @@ $$
 
 <p>We list here some other useful relations we may encounter (recall that vectors are defined by boldfaced low-key letters)</p>
 $$
-\frac{\partial (\boldsymbol{b}^T\boldsymbol{a})}{\partial \boldsymbol{a}} = \boldsymbol{b},
+\frac{\partial (\boldsymbol{x}^T\boldsymbol{a})}{\partial \boldsymbol{x}} = \boldsymbol{a}^T,
 $$
 
+$$
+\frac{\partial (\boldsymbol{a}^T\boldsymbol{x})}{\partial \boldsymbol{x}} = \boldsymbol{a}^T,
+$$
+
+
 $$
 \frac{\partial tr(\boldsymbol{B}\boldsymbol{A})}{\partial \boldsymbol{A}} = \boldsymbol{B}^T,
 $$
diff --git a/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz b/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz
index 2a9642d24..49dc5e02d 100644
Binary files a/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz and b/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz differ
diff --git a/doc/pub/week35/ipynb/week35.ipynb b/doc/pub/week35/ipynb/week35.ipynb
index d2fd55c69..7ce405ac8 100644
--- a/doc/pub/week35/ipynb/week35.ipynb
+++ b/doc/pub/week35/ipynb/week35.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "7d46aac3",
+   "id": "d1a45cb9",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c2e822c3",
+   "id": "df0b160c",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8fe173b0",
+   "id": "5480a93a",
    "metadata": {
     "editable": true
    },
@@ -49,7 +49,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3d8f7c5e",
+   "id": "6d7042d6",
    "metadata": {
     "editable": true
    },
@@ -69,7 +69,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "136f0fb9",
+   "id": "f38f6344",
    "metadata": {
     "editable": true
    },
@@ -103,7 +103,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "81e34904",
+   "id": "88321305",
    "metadata": {
     "editable": true
    },
@@ -119,7 +119,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9eb8c3c0",
+   "id": "b3902f8c",
    "metadata": {
     "editable": true
    },
@@ -131,7 +131,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b57a761c",
+   "id": "6cc9fd26",
    "metadata": {
     "editable": true
    },
@@ -141,7 +141,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a1938870",
+   "id": "083c1a6b",
    "metadata": {
     "editable": true
    },
@@ -153,7 +153,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4dfd5db",
+   "id": "38b6975b",
    "metadata": {
     "editable": true
    },
@@ -174,7 +174,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eb46d019",
+   "id": "8a65b0a7",
    "metadata": {
     "editable": true
    },
@@ -186,7 +186,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97bb0d9d",
+   "id": "7097614a",
    "metadata": {
     "editable": true
    },
@@ -199,7 +199,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "70a33137",
+   "id": "d57cdf7e",
    "metadata": {
     "editable": true
    },
@@ -211,7 +211,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc9a57c9",
+   "id": "8ee5538d",
    "metadata": {
     "editable": true
    },
@@ -223,7 +223,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fd395098",
+   "id": "09ce36b5",
    "metadata": {
     "editable": true
    },
@@ -233,7 +233,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6c37190",
+   "id": "3884daa6",
    "metadata": {
     "editable": true
    },
@@ -245,7 +245,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3754a599",
+   "id": "046f3817",
    "metadata": {
     "editable": true
    },
@@ -258,7 +258,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eb1e5c6a",
+   "id": "327fd863",
    "metadata": {
     "editable": true
    },
@@ -270,7 +270,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c5bab63d",
+   "id": "d2df2b68",
    "metadata": {
     "editable": true
    },
@@ -280,7 +280,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "469d828a",
+   "id": "e5b6d8a1",
    "metadata": {
     "editable": true
    },
@@ -292,7 +292,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "99cb3e0c",
+   "id": "f40f76e8",
    "metadata": {
     "editable": true
    },
@@ -304,7 +304,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a313d648",
+   "id": "b7b515ea",
    "metadata": {
     "editable": true
    },
@@ -315,7 +315,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45638946",
+   "id": "915095bd",
    "metadata": {
     "editable": true
    },
@@ -327,7 +327,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b8130f9c",
+   "id": "d1dd8cbd",
    "metadata": {
     "editable": true
    },
@@ -346,7 +346,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c2a5f5ad",
+   "id": "1530e93c",
    "metadata": {
     "editable": true
    },
@@ -359,7 +359,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7385a922",
+   "id": "e96b563a",
    "metadata": {
     "editable": true
    },
@@ -369,7 +369,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3413e2f",
+   "id": "982d1604",
    "metadata": {
     "editable": true
    },
@@ -381,7 +381,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3349093c",
+   "id": "32a75225",
    "metadata": {
     "editable": true
    },
@@ -391,7 +391,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a33ba2e",
+   "id": "54f26dca",
    "metadata": {
     "editable": true
    },
@@ -403,7 +403,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a6045f4",
+   "id": "4310cf8b",
    "metadata": {
     "editable": true
    },
@@ -413,7 +413,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b311171",
+   "id": "7f7dd61f",
    "metadata": {
     "editable": true
    },
@@ -425,7 +425,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "558d3b32",
+   "id": "f18dbba1",
    "metadata": {
     "editable": true
    },
@@ -436,7 +436,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "deffceee",
+   "id": "6b6d945a",
    "metadata": {
     "editable": true
    },
@@ -448,7 +448,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fffc54ec",
+   "id": "7a1244bc",
    "metadata": {
     "editable": true
    },
@@ -458,7 +458,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f492262",
+   "id": "87368735",
    "metadata": {
     "editable": true
    },
@@ -470,7 +470,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8d378b38",
+   "id": "c9a49592",
    "metadata": {
     "editable": true
    },
@@ -480,7 +480,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "539d62f8",
+   "id": "3f2233cd",
    "metadata": {
     "editable": true
    },
@@ -492,7 +492,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "238a8e6d",
+   "id": "7393b1df",
    "metadata": {
     "editable": true
    },
@@ -512,7 +512,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "29e68d43",
+   "id": "16eb1cab",
    "metadata": {
     "editable": true
    },
@@ -539,7 +539,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b2ff1ac",
+   "id": "fadb6c5f",
    "metadata": {
     "editable": true
    },
@@ -551,7 +551,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "296d789f",
+   "id": "1b226a3b",
    "metadata": {
     "editable": true
    },
@@ -563,7 +563,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77190213",
+   "id": "8835682a",
    "metadata": {
     "editable": true
    },
@@ -579,7 +579,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c908c476",
+   "id": "94ea8746",
    "metadata": {
     "editable": true
    },
@@ -597,7 +597,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6df5bf4",
+   "id": "e8a3e5ff",
    "metadata": {
     "editable": true
    },
@@ -609,7 +609,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "825ed674",
+   "id": "2aeb647a",
    "metadata": {
     "editable": true
    },
@@ -621,7 +621,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ba708b07",
+   "id": "c1a9041d",
    "metadata": {
     "editable": true
    },
@@ -632,7 +632,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e7515806",
+   "id": "7d68af48",
    "metadata": {
     "editable": true
    },
@@ -644,7 +644,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec27da02",
+   "id": "3f16856a",
    "metadata": {
     "editable": true
    },
@@ -654,7 +654,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0e568f9b",
+   "id": "6b5f1f53",
    "metadata": {
     "editable": true
    },
@@ -666,7 +666,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50b3c398",
+   "id": "cdc1e2de",
    "metadata": {
     "editable": true
    },
@@ -680,7 +680,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f67a6838",
+   "id": "f2d5e2ac",
    "metadata": {
     "editable": true
    },
@@ -692,7 +692,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "27095386",
+   "id": "6100c9ac",
    "metadata": {
     "editable": true
    },
@@ -704,7 +704,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97e6e136",
+   "id": "e4ca2a6c",
    "metadata": {
     "editable": true
    },
@@ -716,41 +716,41 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2f2cb2f1",
+   "id": "7af8ed53",
    "metadata": {
     "editable": true
    },
    "source": [
-    "which means that (using our previous example) we have"
+    "which means that (using our previous example and keeping track of our definition of the derivative of a scalar) we have"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "19160cb4",
+   "id": "969a360f",
    "metadata": {
     "editable": true
    },
    "source": [
     "$$\n",
-    "\\frac{\\partial \\alpha}{\\partial \\boldsymbol{x}} = \\boldsymbol{z}=\\boldsymbol{A}^T\\boldsymbol{y}.\n",
+    "\\frac{\\partial \\alpha}{\\partial \\boldsymbol{x}} = \\frac{\\partial \\boldsymbol{z}^T\\boldsymbol{x}}{\\partial \\boldsymbol{x}}=\\boldsymbol{z}^T=\\boldsymbol{A}^T\\boldsymbol{y}.\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "50ff8918",
+   "id": "bb94df46",
    "metadata": {
     "editable": true
    },
    "source": [
     "Note that the resulting vector elements are the same for $\\boldsymbol{z}^T$ and $\\boldsymbol{z}$, the only difference is that one is just the transpose of the other.\n",
     "\n",
-    "Since $\\alpha$ is a scalar we have $\\alpha =\\alpha^T=\\boldsymbol{x}^T\\boldsymbol{A}^T\\boldsymbol{y}$. Defining now $\\boldsymbol{z}=\\boldsymbol{x}^T\\boldsymbol{A}^T$ we find that"
+    "Since $\\alpha$ is a scalar we have $\\alpha =\\alpha^T=\\boldsymbol{x}^T\\boldsymbol{A}^T\\boldsymbol{y}$. Defining now $\\boldsymbol{z}^T=\\boldsymbol{x}^T\\boldsymbol{A}^T$ we find that"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "615fbba5",
+   "id": "6415e688",
    "metadata": {
     "editable": true
    },
@@ -762,7 +762,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4116f7dd",
+   "id": "5b3b1ecd",
    "metadata": {
     "editable": true
    },
@@ -776,7 +776,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2ee0f30c",
+   "id": "a986474a",
    "metadata": {
     "editable": true
    },
@@ -788,7 +788,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bd14b926",
+   "id": "af874fe9",
    "metadata": {
     "editable": true
    },
@@ -800,7 +800,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5b7c9517",
+   "id": "074b1322",
    "metadata": {
     "editable": true
    },
@@ -812,7 +812,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2a8bb990",
+   "id": "e8120e11",
    "metadata": {
     "editable": true
    },
@@ -822,7 +822,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5e4cee2a",
+   "id": "5c4a9f64",
    "metadata": {
     "editable": true
    },
@@ -834,7 +834,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "32358c8c",
+   "id": "7a99ee98",
    "metadata": {
     "editable": true
    },
@@ -844,7 +844,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "582e5dd2",
+   "id": "d4d80443",
    "metadata": {
     "editable": true
    },
@@ -856,7 +856,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "09021946",
+   "id": "8faa132f",
    "metadata": {
     "editable": true
    },
@@ -866,7 +866,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1996c675",
+   "id": "cbb38e2d",
    "metadata": {
     "editable": true
    },
@@ -878,7 +878,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "21a8f52b",
+   "id": "c57d10e0",
    "metadata": {
     "editable": true
    },
@@ -890,7 +890,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "750c017f",
+   "id": "7acf1bc0",
    "metadata": {
     "editable": true
    },
@@ -902,7 +902,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ad136af2",
+   "id": "0268eb52",
    "metadata": {
     "editable": true
    },
@@ -917,7 +917,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "afac1035",
+   "id": "60003495",
    "metadata": {
     "editable": true
    },
@@ -929,7 +929,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b7bf070",
+   "id": "87737af5",
    "metadata": {
     "editable": true
    },
@@ -939,7 +939,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2670dafb",
+   "id": "172d2360",
    "metadata": {
     "editable": true
    },
@@ -951,7 +951,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "63337734",
+   "id": "7c8b553e",
    "metadata": {
     "editable": true
    },
@@ -961,7 +961,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bda0b6b2",
+   "id": "a83a35b7",
    "metadata": {
     "editable": true
    },
@@ -973,7 +973,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "db44d551",
+   "id": "7ad0a8e7",
    "metadata": {
     "editable": true
    },
@@ -983,7 +983,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a389e623",
+   "id": "11c08e7b",
    "metadata": {
     "editable": true
    },
@@ -995,7 +995,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a8e046db",
+   "id": "03529c8d",
    "metadata": {
     "editable": true
    },
@@ -1007,7 +1007,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "074cc965",
+   "id": "5eb85448",
    "metadata": {
     "editable": true
    },
@@ -1019,7 +1019,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fca52100",
+   "id": "fee9b6de",
    "metadata": {
     "editable": true
    },
@@ -1029,7 +1029,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9c56f854",
+   "id": "3fa355af",
    "metadata": {
     "editable": true
    },
@@ -1041,7 +1041,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a556df3",
+   "id": "db643ace",
    "metadata": {
     "editable": true
    },
@@ -1054,7 +1054,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "67239adf",
+   "id": "482c681d",
    "metadata": {
     "editable": true
    },
@@ -1066,7 +1066,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a10c57f5",
+   "id": "d9ae3be7",
    "metadata": {
     "editable": true
    },
@@ -1076,7 +1076,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a7c13076",
+   "id": "edc496c8",
    "metadata": {
     "editable": true
    },
@@ -1088,7 +1088,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "db2e932a",
+   "id": "964a61c9",
    "metadata": {
     "editable": true
    },
@@ -1098,7 +1098,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b001a262",
+   "id": "d1c8b642",
    "metadata": {
     "editable": true
    },
@@ -1110,7 +1110,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c4ec2cb7",
+   "id": "14b971fc",
    "metadata": {
     "editable": true
    },
@@ -1120,7 +1120,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "35bba0f9",
+   "id": "2213cf00",
    "metadata": {
     "editable": true
    },
@@ -1132,7 +1132,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39d2d221",
+   "id": "f27f0729",
    "metadata": {
     "editable": true
    },
@@ -1142,7 +1142,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a18b7bb",
+   "id": "b5e3559a",
    "metadata": {
     "editable": true
    },
@@ -1154,7 +1154,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d22d6836",
+   "id": "6e4ee9c5",
    "metadata": {
     "editable": true
    },
@@ -1164,7 +1164,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "567161ac",
+   "id": "e767c78d",
    "metadata": {
     "editable": true
    },
@@ -1176,7 +1176,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28e3d37b",
+   "id": "2607f6ad",
    "metadata": {
     "editable": true
    },
@@ -1188,19 +1188,31 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e42fd086",
+   "id": "eaf435b4",
    "metadata": {
     "editable": true
    },
    "source": [
     "$$\n",
-    "\\frac{\\partial (\\boldsymbol{b}^T\\boldsymbol{a})}{\\partial \\boldsymbol{a}} = \\boldsymbol{b},\n",
+    "\\frac{\\partial (\\boldsymbol{x}^T\\boldsymbol{a})}{\\partial \\boldsymbol{x}} = \\boldsymbol{a}^T,\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "8fc99a0c",
+   "id": "2a2ee3ae",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\frac{\\partial (\\boldsymbol{a}^T\\boldsymbol{x})}{\\partial \\boldsymbol{x}} = \\boldsymbol{a}^T,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3ef4947e",
    "metadata": {
     "editable": true
    },
@@ -1212,7 +1224,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "86d74fd9",
+   "id": "00b849f0",
    "metadata": {
     "editable": true
    },
@@ -1224,7 +1236,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "554b9a43",
+   "id": "4f2d2dfa",
    "metadata": {
     "editable": true
    },
@@ -1240,7 +1252,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1affa7d",
+   "id": "3d2dcac2",
    "metadata": {
     "editable": true
    },
@@ -1252,7 +1264,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cf2e3528",
+   "id": "c7c9832d",
    "metadata": {
     "editable": true
    },
@@ -1262,7 +1274,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9bfab245",
+   "id": "75019e89",
    "metadata": {
     "editable": true
    },
@@ -1274,7 +1286,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4e923312",
+   "id": "5b04e748",
    "metadata": {
     "editable": true
    },
@@ -1292,7 +1304,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ae25f416",
+   "id": "223893ea",
    "metadata": {
     "editable": true
    },
@@ -1304,7 +1316,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d616c204",
+   "id": "621b7821",
    "metadata": {
     "editable": true
    },
@@ -1316,7 +1328,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c767f7d8",
+   "id": "d5dc18bb",
    "metadata": {
     "editable": true
    },
@@ -1326,7 +1338,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5e10686f",
+   "id": "136df89f",
    "metadata": {
     "editable": true
    },
@@ -1338,7 +1350,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0d8fd143",
+   "id": "3b19fd49",
    "metadata": {
     "editable": true
    },
@@ -1348,7 +1360,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bf85a0ca",
+   "id": "ae5dc063",
    "metadata": {
     "editable": true
    },
@@ -1360,7 +1372,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f8625113",
+   "id": "3eee6878",
    "metadata": {
     "editable": true
    },
@@ -1370,7 +1382,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ca3f31df",
+   "id": "98881e46",
    "metadata": {
     "editable": true
    },
@@ -1384,7 +1396,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "32f2e67e",
+   "id": "2d21b7e5",
    "metadata": {
     "editable": true
    },
@@ -1396,7 +1408,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0571367",
+   "id": "b0cb659a",
    "metadata": {
     "editable": true
    },
@@ -1407,7 +1419,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6199aacb",
+   "id": "86aaa708",
    "metadata": {
     "editable": true
    },
@@ -1420,7 +1432,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "e17aecdf",
+   "id": "12dc0e7b",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1447,7 +1459,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "295f958b",
+   "id": "ced073c0",
    "metadata": {
     "editable": true
    },
@@ -1458,7 +1470,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "da33d84b",
+   "id": "9b252462",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1471,7 +1483,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f8656ecc",
+   "id": "acd397d0",
    "metadata": {
     "editable": true
    },
@@ -1485,7 +1497,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "10bb7d14",
+   "id": "c2cd60aa",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1498,7 +1510,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43fef194",
+   "id": "69a875cd",
    "metadata": {
     "editable": true
    },
@@ -1509,7 +1521,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "c7b2d7e8",
+   "id": "648deb3f",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1521,7 +1533,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3704aaf9",
+   "id": "6ba117de",
    "metadata": {
     "editable": true
    },
@@ -1532,7 +1544,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "0942d279",
+   "id": "53a84803",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1548,7 +1560,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a8d0b4f2",
+   "id": "b63a7058",
    "metadata": {
     "editable": true
    },
@@ -1559,7 +1571,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "6d95666b",
+   "id": "20110f9a",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1573,7 +1585,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77262b73",
+   "id": "b302b9c5",
    "metadata": {
     "editable": true
    },
@@ -1594,7 +1606,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "07ecffe3",
+   "id": "04b5adc1",
    "metadata": {
     "editable": true
    },
@@ -1605,7 +1617,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "6bb953ea",
+   "id": "6c5d7761",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1658,7 +1670,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b6523939",
+   "id": "ac8ecd6e",
    "metadata": {
     "editable": true
    },
@@ -1669,7 +1681,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "33d42837",
+   "id": "cc36d2bf",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1694,7 +1706,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2ff685c2",
+   "id": "45aaee74",
    "metadata": {
     "editable": true
    },
@@ -1706,7 +1718,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4bdd8f8b",
+   "id": "28a9e9a1",
    "metadata": {
     "editable": true
    },
@@ -1735,7 +1747,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b663d865",
+   "id": "2a33a638",
    "metadata": {
     "editable": true
    },
@@ -1760,7 +1772,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a49bbab2",
+   "id": "21229aa6",
    "metadata": {
     "editable": true
    },
@@ -1780,7 +1792,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d04ab36",
+   "id": "1a8c3ef5",
    "metadata": {
     "editable": true
    },
@@ -1807,7 +1819,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7694b847",
+   "id": "fa17153a",
    "metadata": {
     "editable": true
    },
@@ -1820,7 +1832,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3bee616",
+   "id": "f52cd539",
    "metadata": {
     "editable": true
    },
@@ -1832,7 +1844,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2d8765c8",
+   "id": "75f53c7e",
    "metadata": {
     "editable": true
    },
@@ -1843,7 +1855,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "372b1ac9",
+   "id": "069ab299",
    "metadata": {
     "editable": true
    },
@@ -1859,7 +1871,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "91b59881",
+   "id": "48ff7059",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1893,7 +1905,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "752bdf5c",
+   "id": "73e38f33",
    "metadata": {
     "editable": true
    },
@@ -1903,7 +1915,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b448d7a7",
+   "id": "f91e0055",
    "metadata": {
     "editable": true
    },
@@ -1918,7 +1930,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c44bc2b9",
+   "id": "92015a76",
    "metadata": {
     "editable": true
    },
@@ -1930,7 +1942,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "316b55f9",
+   "id": "ebafe28e",
    "metadata": {
     "editable": true
    },
@@ -1940,7 +1952,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "649ae921",
+   "id": "27b3c9e2",
    "metadata": {
     "editable": true
    },
@@ -1956,7 +1968,7 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "7105b779",
+   "id": "7d98302c",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1973,7 +1985,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc901b3e",
+   "id": "8083ffaf",
    "metadata": {
     "editable": true
    },
@@ -1986,7 +1998,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "a3f97306",
+   "id": "74135af6",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2033,7 +2045,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "92e55bd9",
+   "id": "3867175f",
    "metadata": {
     "editable": true
    },
@@ -2044,7 +2056,7 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "eb0f9eeb",
+   "id": "145ec792",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2147,7 +2159,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7eef8cc6",
+   "id": "dd2e26c6",
    "metadata": {
     "editable": true
    },
@@ -2175,7 +2187,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "929f1ffa",
+   "id": "8f6f5e14",
    "metadata": {
     "editable": true
    },
@@ -2210,7 +2222,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1cf95ac7",
+   "id": "a2bb8567",
    "metadata": {
     "editable": true
    },
@@ -2225,7 +2237,7 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "ccf5197e",
+   "id": "5ce4bb30",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2250,7 +2262,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4bc3b8e7",
+   "id": "9899b102",
    "metadata": {
     "editable": true
    },
@@ -2266,7 +2278,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "832c9186",
+   "id": "940f1206",
    "metadata": {
     "editable": true
    },
@@ -2278,7 +2290,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33936009",
+   "id": "03bf3859",
    "metadata": {
     "editable": true
    },
@@ -2293,7 +2305,7 @@
   },
   {
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-   "id": "a33c046a",
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@@ -2305,7 +2317,7 @@
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@@ -2315,7 +2327,7 @@
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@@ -2327,7 +2339,7 @@
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@@ -2337,7 +2349,7 @@
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@@ -2349,7 +2361,7 @@
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@@ -2362,7 +2374,7 @@
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@@ -2374,7 +2386,7 @@
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@@ -2384,7 +2396,7 @@
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@@ -2396,7 +2408,7 @@
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@@ -2406,7 +2418,7 @@
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@@ -2418,7 +2430,7 @@
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@@ -2428,7 +2440,7 @@
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@@ -2440,7 +2452,7 @@
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@@ -2450,7 +2462,7 @@
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@@ -2462,7 +2474,7 @@
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@@ -2472,7 +2484,7 @@
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@@ -2484,7 +2496,7 @@
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@@ -2494,7 +2506,7 @@
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@@ -2506,7 +2518,7 @@
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@@ -2518,7 +2530,7 @@
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@@ -2530,7 +2542,7 @@
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@@ -2543,7 +2555,7 @@
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@@ -2555,7 +2567,7 @@
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@@ -2565,7 +2577,7 @@
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@@ -2579,7 +2591,7 @@
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@@ -2676,7 +2688,7 @@
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@@ -2697,7 +2709,7 @@
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@@ -2709,7 +2721,7 @@
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@@ -2719,7 +2731,7 @@
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@@ -2731,7 +2743,7 @@
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@@ -2741,7 +2753,7 @@
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@@ -2753,7 +2765,7 @@
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@@ -2769,7 +2781,7 @@
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@@ -2779,7 +2791,7 @@
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@@ -2793,7 +2805,7 @@
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@@ -2805,7 +2817,7 @@
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@@ -2817,7 +2829,7 @@
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@@ -2829,7 +2841,7 @@
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@@ -2839,7 +2851,7 @@
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@@ -2851,7 +2863,7 @@
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@@ -2861,7 +2873,7 @@
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@@ -2873,7 +2885,7 @@
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@@ -2884,7 +2896,7 @@
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@@ -2896,7 +2908,7 @@
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@@ -2908,7 +2920,7 @@
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@@ -2918,7 +2930,7 @@
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@@ -2930,7 +2942,7 @@
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@@ -2942,7 +2954,7 @@
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@@ -2952,7 +2964,7 @@
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@@ -2964,7 +2976,7 @@
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@@ -2974,7 +2986,7 @@
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@@ -2986,7 +2998,7 @@
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@@ -2996,7 +3008,7 @@
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@@ -3036,7 +3048,7 @@
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@@ -3053,7 +3065,7 @@
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@@ -3076,7 +3088,7 @@
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@@ -3093,7 +3105,7 @@
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@@ -3112,7 +3124,7 @@
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@@ -3123,7 +3135,7 @@
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@@ -3135,7 +3147,7 @@
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@@ -3153,7 +3165,7 @@
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@@ -3169,7 +3181,7 @@
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@@ -3181,7 +3193,7 @@
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@@ -3191,7 +3203,7 @@
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@@ -3206,7 +3218,7 @@
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@@ -3218,7 +3230,7 @@
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@@ -3228,7 +3240,7 @@
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@@ -3240,7 +3252,7 @@
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@@ -3250,7 +3262,7 @@
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@@ -3262,7 +3274,7 @@
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@@ -3274,7 +3286,7 @@
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@@ -3289,7 +3301,7 @@
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@@ -3300,7 +3312,7 @@
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@@ -3320,7 +3332,7 @@
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@@ -3332,7 +3344,7 @@
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@@ -3342,7 +3354,7 @@
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@@ -3354,7 +3366,7 @@
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@@ -3383,7 +3395,7 @@
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@@ -3410,7 +3422,7 @@
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@@ -3421,7 +3433,7 @@
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@@ -3461,7 +3473,7 @@
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@@ -3478,7 +3490,7 @@
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@@ -3501,7 +3513,7 @@
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@@ -3515,7 +3527,7 @@
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@@ -3534,7 +3546,7 @@
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@@ -3544,7 +3556,7 @@
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@@ -3556,7 +3568,7 @@
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@@ -3570,7 +3582,7 @@
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@@ -3582,7 +3594,7 @@
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@@ -3592,7 +3604,7 @@
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@@ -3604,7 +3616,7 @@
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@@ -3621,7 +3633,7 @@
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@@ -3631,7 +3643,7 @@
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@@ -3647,7 +3659,7 @@
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@@ -3657,7 +3669,7 @@
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@@ -3673,7 +3685,7 @@
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@@ -3683,7 +3695,7 @@
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@@ -3699,7 +3711,7 @@
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@@ -3709,7 +3721,7 @@
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@@ -3726,7 +3738,7 @@
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@@ -3738,7 +3750,7 @@
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@@ -3750,7 +3762,7 @@
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@@ -3772,7 +3784,7 @@
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@@ -3784,7 +3796,7 @@
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@@ -3796,7 +3808,7 @@
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@@ -3808,7 +3820,7 @@
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@@ -3818,7 +3830,7 @@
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@@ -3830,7 +3842,7 @@
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@@ -3840,7 +3852,7 @@
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@@ -3852,7 +3864,7 @@
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@@ -3868,7 +3880,7 @@
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@@ -3880,7 +3892,7 @@
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@@ -3892,7 +3904,7 @@
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@@ -3902,7 +3914,7 @@
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@@ -3914,7 +3926,7 @@
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@@ -3925,7 +3937,7 @@
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@@ -3937,7 +3949,7 @@
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@@ -3947,7 +3959,7 @@
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@@ -3959,7 +3971,7 @@
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@@ -3969,7 +3981,7 @@
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@@ -3981,7 +3993,7 @@
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@@ -3992,7 +4004,7 @@
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@@ -4004,7 +4016,7 @@
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@@ -4022,7 +4034,7 @@
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@@ -4038,7 +4050,7 @@
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@@ -4050,7 +4062,7 @@
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@@ -4062,7 +4074,7 @@
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@@ -4074,7 +4086,7 @@
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@@ -4087,7 +4099,7 @@
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@@ -4103,7 +4115,7 @@
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@@ -4117,7 +4129,7 @@
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@@ -4127,7 +4139,7 @@
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@@ -4139,7 +4151,7 @@
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@@ -4149,7 +4161,7 @@
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@@ -4161,7 +4173,7 @@
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@@ -4171,7 +4183,7 @@
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@@ -4185,7 +4197,7 @@
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@@ -4202,7 +4214,7 @@
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@@ -4218,7 +4230,7 @@
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@@ -4230,7 +4242,7 @@
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@@ -4243,7 +4255,7 @@
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@@ -4257,7 +4269,7 @@
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@@ -4267,7 +4279,7 @@
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@@ -4280,7 +4292,7 @@
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@@ -4299,7 +4311,7 @@
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@@ -4311,7 +4323,7 @@
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@@ -4323,7 +4335,7 @@
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@@ -4333,7 +4345,7 @@
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@@ -4345,7 +4357,7 @@
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@@ -4358,7 +4370,7 @@
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@@ -4377,7 +4389,7 @@
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@@ -4387,7 +4399,7 @@
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@@ -4406,7 +4418,7 @@
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@@ -4424,7 +4436,7 @@
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@@ -4438,7 +4450,7 @@
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@@ -4453,7 +4465,7 @@
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@@ -4474,7 +4486,7 @@
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@@ -4491,7 +4503,7 @@
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@@ -4523,7 +4535,7 @@
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@@ -4537,7 +4549,7 @@
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@@ -4550,7 +4562,7 @@
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@@ -4575,7 +4587,7 @@
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@@ -4585,7 +4597,7 @@
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@@ -4596,7 +4608,7 @@
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@@ -4650,7 +4662,7 @@
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@@ -4667,7 +4679,7 @@
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@@ -4679,7 +4691,7 @@
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@@ -4691,7 +4703,7 @@
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@@ -4701,7 +4713,7 @@
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@@ -4718,7 +4730,7 @@
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@@ -4728,7 +4740,7 @@
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@@ -4743,7 +4755,7 @@
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@@ -4753,7 +4765,7 @@
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@@ -4767,7 +4779,7 @@
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@@ -4779,7 +4791,7 @@
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@@ -4791,7 +4803,7 @@
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@@ -4803,7 +4815,7 @@
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@@ -4813,7 +4825,7 @@
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@@ -4825,7 +4837,7 @@
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@@ -4835,7 +4847,7 @@
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@@ -4852,7 +4864,7 @@
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@@ -4862,7 +4874,7 @@
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@@ -4874,7 +4886,7 @@
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@@ -4884,7 +4896,7 @@
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@@ -4896,7 +4908,7 @@
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@@ -4910,7 +4922,7 @@
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@@ -4922,7 +4934,7 @@
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@@ -4944,7 +4956,7 @@
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@@ -4956,7 +4968,7 @@
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@@ -4971,7 +4983,7 @@
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@@ -4983,7 +4995,7 @@
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@@ -4995,7 +5007,7 @@
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@@ -5005,7 +5017,7 @@
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@@ -5017,7 +5029,7 @@
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@@ -5027,7 +5039,7 @@
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@@ -5039,7 +5051,7 @@
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@@ -5049,7 +5061,7 @@
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@@ -5061,7 +5073,7 @@
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@@ -5078,7 +5090,7 @@
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@@ -5091,7 +5103,7 @@
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@@ -5103,7 +5115,7 @@
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@@ -5113,7 +5125,7 @@
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   {
    "cell_type": "markdown",
-   "id": "201d905c",
+   "id": "c2196256",
    "metadata": {
     "editable": true
    },
@@ -5126,7 +5138,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f63bcc7",
+   "id": "aa745e43",
    "metadata": {
     "editable": true
    },
@@ -5136,7 +5148,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0e39045a",
+   "id": "cddbb44b",
    "metadata": {
     "editable": true
    },
@@ -5148,7 +5160,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28779e57",
+   "id": "3bd6cdd9",
    "metadata": {
     "editable": true
    },
@@ -5161,7 +5173,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d7d76fd0",
+   "id": "980af216",
    "metadata": {
     "editable": true
    },
@@ -5174,7 +5186,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a2113041",
+   "id": "22b679ba",
    "metadata": {
     "editable": true
    },
@@ -5186,7 +5198,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "41d877da",
+   "id": "190052a7",
    "metadata": {
     "editable": true
    },
@@ -5198,7 +5210,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f7beeed5",
+   "id": "ad1528bc",
    "metadata": {
     "editable": true
    },
@@ -5208,7 +5220,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6dc01d3f",
+   "id": "fc69d642",
    "metadata": {
     "editable": true
    },
@@ -5221,7 +5233,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8fbaf3ed",
+   "id": "387716c0",
    "metadata": {
     "editable": true
    },
@@ -5233,7 +5245,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "200e98c8",
+   "id": "8d57c0a0",
    "metadata": {
     "editable": true
    },
@@ -5245,7 +5257,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7ac27cfd",
+   "id": "13455d46",
    "metadata": {
     "editable": true
    },
@@ -5257,7 +5269,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bf696c60",
+   "id": "3bbc2f00",
    "metadata": {
     "editable": true
    },
@@ -5269,7 +5281,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d4bcd70",
+   "id": "b7daee88",
    "metadata": {
     "editable": true
    },
@@ -5283,7 +5295,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "516462d4",
+   "id": "1299b1c5",
    "metadata": {
     "editable": true
    },
@@ -5295,7 +5307,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9ce7b51b",
+   "id": "db23d56c",
    "metadata": {
     "editable": true
    },
@@ -5305,7 +5317,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b0cec572",
+   "id": "b6b71f2b",
    "metadata": {
     "editable": true
    },
@@ -5317,7 +5329,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "67b0fa4b",
+   "id": "a126967a",
    "metadata": {
     "editable": true
    },
@@ -5329,7 +5341,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee32bb17",
+   "id": "45a67a1a",
    "metadata": {
     "editable": true
    },
@@ -5341,7 +5353,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "78f724ed",
+   "id": "efe0de6c",
    "metadata": {
     "editable": true
    },
@@ -5353,7 +5365,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8cb8bdac",
+   "id": "8860fc43",
    "metadata": {
     "editable": true
    },
@@ -5365,7 +5377,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "89e76a8c",
+   "id": "5b14ec49",
    "metadata": {
     "editable": true
    },
@@ -5384,7 +5396,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "109178a9",
+   "id": "fa58f8d1",
    "metadata": {
     "editable": true
    },
@@ -5396,7 +5408,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5533200d",
+   "id": "848a33e8",
    "metadata": {
     "editable": true
    },
@@ -5406,7 +5418,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c9af410a",
+   "id": "45cbaee4",
    "metadata": {
     "editable": true
    },
@@ -5418,7 +5430,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f14775b0",
+   "id": "c691de3f",
    "metadata": {
     "editable": true
    },
@@ -5428,7 +5440,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7712331b",
+   "id": "c7e337f4",
    "metadata": {
     "editable": true
    },
@@ -5440,7 +5452,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "81c01b03",
+   "id": "8d417ae8",
    "metadata": {
     "editable": true
    },
@@ -5452,7 +5464,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2b34266",
+   "id": "386aa637",
    "metadata": {
     "editable": true
    },
@@ -5468,7 +5480,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e0b093d",
+   "id": "55185be4",
    "metadata": {
     "editable": true
    },
@@ -5480,7 +5492,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8f16e085",
+   "id": "2a7fcef6",
    "metadata": {
     "editable": true
    },
@@ -5492,7 +5504,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ad5bae5",
+   "id": "2f2c4c1d",
    "metadata": {
     "editable": true
    },
@@ -5502,7 +5514,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "763aafea",
+   "id": "e3bab558",
    "metadata": {
     "editable": true
    },
@@ -5514,7 +5526,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7344b28f",
+   "id": "bb50e5e7",
    "metadata": {
     "editable": true
    },
@@ -5524,7 +5536,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bd0aa93e",
+   "id": "6e1bf6c6",
    "metadata": {
     "editable": true
    },
@@ -5536,7 +5548,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58b92564",
+   "id": "6089b625",
    "metadata": {
     "editable": true
    },
@@ -5553,7 +5565,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9c8672be",
+   "id": "68df3751",
    "metadata": {
     "editable": true
    },
@@ -5565,7 +5577,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "11590d10",
+   "id": "60e8783d",
    "metadata": {
     "editable": true
    },
@@ -5577,7 +5589,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4c46b518",
+   "id": "75eaf332",
    "metadata": {
     "editable": true
    },
@@ -5587,7 +5599,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b0da6a21",
+   "id": "d98940a5",
    "metadata": {
     "editable": true
    },
@@ -5599,7 +5611,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b34e073",
+   "id": "3a2a3500",
    "metadata": {
     "editable": true
    },
@@ -5609,7 +5621,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "029f1aa5",
+   "id": "ea6ff87d",
    "metadata": {
     "editable": true
    },
@@ -5621,7 +5633,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "49079af3",
+   "id": "eb7270da",
    "metadata": {
     "editable": true
    },
@@ -5631,7 +5643,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "735e9f4c",
+   "id": "1626b163",
    "metadata": {
     "editable": true
    },
@@ -5643,7 +5655,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fccfd6ca",
+   "id": "5182459c",
    "metadata": {
     "editable": true
    },
@@ -5653,7 +5665,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2aa75180",
+   "id": "951dec6f",
    "metadata": {
     "editable": true
    },
@@ -5665,7 +5677,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bad889e8",
+   "id": "f09e051d",
    "metadata": {
     "editable": true
    },
diff --git a/doc/src/week35/week35.do.txt b/doc/src/week35/week35.do.txt
index 9a5427154..0b0255015 100644
--- a/doc/src/week35/week35.do.txt
+++ b/doc/src/week35/week35.do.txt
@@ -315,16 +315,16 @@ $\bm{z}^T=\bm{y}^T\bm{A}$, a vector of length $n$. We have then, using the defin
 \alpha = \bm{z}^T\bm{x},
 \]
 !et
-which means that (using our previous example) we have
+which means that (using our previous example and keeping track of our definition of the derivative of a scalar) we have
 !bt
 \[
-\frac{\partial \alpha}{\partial \bm{x}} = \bm{z}=\bm{A}^T\bm{y}.
+\frac{\partial \alpha}{\partial \bm{x}} = \frac{\partial \bm{z}^T\bm{x}}{\partial \bm{x}}=\bm{z}^T=\bm{A}^T\bm{y}.
 \]
 !et
 
 Note that the resulting vector elements are the same for $\bm{z}^T$ and $\bm{z}$, the only difference is that one is just the transpose of the other.
 
-Since $\alpha$ is a scalar we have $\alpha =\alpha^T=\bm{x}^T\bm{A}^T\bm{y}$. Defining now $\bm{z}=\bm{x}^T\bm{A}^T$ we find that
+Since $\alpha$ is a scalar we have $\alpha =\alpha^T=\bm{x}^T\bm{A}^T\bm{y}$. Defining now $\bm{z}^T=\bm{x}^T\bm{A}^T$ we find that
 !bt
 \[
 \frac{\partial \alpha}{\partial \bm{y}} = \bm{z}^T=\bm{x}^T\bm{A}^T.
@@ -477,9 +477,15 @@ or as
 We list here some other useful relations we may encounter (recall that vectors are defined by boldfaced low-key letters)
 !bt
 \[
-\frac{\partial (\bm{b}^T\bm{a})}{\partial \bm{a}} = \bm{b},
+\frac{\partial (\bm{x}^T\bm{a})}{\partial \bm{x}} = \bm{a}^T,
 \]
 !et
+!bt
+\[
+\frac{\partial (\bm{a}^T\bm{x})}{\partial \bm{x}} = \bm{a}^T,
+\]
+!et
+
 !bt
 \[
 \frac{\partial tr(\bm{B}\bm{A})}{\partial \bm{A}} = \bm{B}^T,