Here’s a thread with links to a lot of material about the derivation of back propagation.
Here’s a series of threads by mentor Jonas Slalin that also cover the math here.
But note that all this is beyond the scope of these courses: Prof Ng has specifically designed these courses not to require calculus knowledge. So the good news is you don’t need to know calculus to succeed here, but the bad news is you have to just accept the formulas as Prof Ng states them.