added to week 35

doc/src/week35/week35.do.txt

@@ -2921,3 +2921,31 @@ and
 \]
 !et
 and finally find the second derivative of this function with respect to the vector $\bm{s}$.
+
+_Hint_: In these exercises it is always useful to write out with summation indices the various quantities.
+As an example, consider the function
+
+!bt
+\[
+f(\bm{x}) =\bm{A}\bm{x},
+\]
+!et
+which reads for a specific component $f_i$ (we define the matrix $\bm{A}$ to have dimension $n\times n$ and the vector $\bm{x} to have length $n$)
+
+!bt
+\[
+f_i =\sum_{j=0}^{n-1}a_{ij}x_j, 
+\]
+!et
+which leads to
+!bt
+\[
+\frac{\partial f_i}{\partial x_j}= a_{ij},
+\]
+!et
+and written out in terms of the vector $\bm{x}$ we have
+!bt
+\[
+\frac{\partial f(\bm{x})}{\partial \bm{x}}= \bm{A}.
+\]
+!et