I have been studying professor Andrew Ng's Machine Learning course on Coursera. Currently, I am trying to prove the formulas for backpropagation, which is mentioned in Week 5 (in this document). Clearly, it mentions that δ(L) = a(L) − y.
However, I have also came across this video on Youtube. In 4:30, it states that δ(3) = -(y - y^) * f'(z(3)), where f is the sigmoid function. Since L = 3 and y^ = a(L), this means that δ(L) = (a(L) - y) * f'(z(L)). I've also derived the equations and got exactly like in the video. But this has an additional "f'(z(L))" term, which is not the same as in Coursera. I have even implemented this equation in the programming assignment for Week 5, but it only works without the term.
So my question is why Coursera's formula didn't have the last term "f'(z(L))" and why the formula works without it? It seems quite irrational to not have the term in the formula. Can anyone help me to explain this, or correct me if I'm wrong? Any help would be greatly appreciated, thanks.