We obtain
δlj=∑k∂C∂zl+1k∂zl+1k∂zlj=∑kδl+1k∂zl+1k∂zlj,and recalling that
zl+1j=Ml∑i=1wl+1ijali+bl+1j,with Ml being the number of nodes in layer l, we obtain
δlj=∑kδl+1kwl+1kjσ′(zlj),This is our final equation.
We are now ready to set up the algorithm for back propagation and learning the weights and biases.