I am confused here , Where does this formula comes from for the derivative of A[L-1].

Prof Ng has specifically designed these courses not to require knowledge of calculus to make it more accessible to everyone. So he does not show the derivations of things that require calculus (matrix calculus in this case). If you have the math background, here’s a thread which gives links to the derivations (This link is also given on the FAQ Thread for DLS, q.v.).