Help Using Backprop Formulas from Deep Learning Book
My mistake was silly. I did not notice in the book that the weight matrices are numbered as the layer they are going into..so my $w^2$ above should be $w^3$ and then the result from the book is $\frac{\partial }{\partial w^3_{11}}=a^2_1(a^3_1-y)\sigma'(z^3_1)$ exactly as calculated by just doing the derivatives.