crucial that you understand the nitty-gritty math here because in a lot of popular deep learning frameworks we have what's called automatic differentiation which does all of this back propagation for you under the hood and you never even see it which is incredible it made training neural networks so much easier you don't have to implement back propagation anymore but it's still important to understand how these work at the foundation which is why we're going through it now ok obviously then you repeat this for every