Summary: the equations of backpropagation L=aC(zL)l=((wl+1)Tl+1)(zl)bjlC=jlwjklC=akl1jl Exercise - Prove Equations (BP3) and (BP4). That completes the proof of the four fundamental equations of backpropagation. The proof may seem complicated. But it's really just the outcome of carefully applying the chain rule. A little less succinctly, we can think of backpropagation as a way of computing the gradient of the cost function by systematically applying the chain rule from multi-variable calculus. That's all there really is to backpropagation - the rest is details. Exercise 2.5.pptx