Making Sense Of Backpropagation Calculus

A complete understanding of neural network mathematics for backpropagation in more complex networks requires an understanding of more esoteric multivariable calculus notions, like the Jacobian. I'll post an article in the future on this once I have a better grasp of the concept itself. But, we can achieve quite a lot of intuition at a slightly more basic level. Turns out that we already did a bulk of the work -- computing backpropagation on a larger neural network just requires a few logical steps. Ignoring the biases, let's see if we can use similar logic to backpropagate through are more complex network, this time to two different weights.