Partial Derivatives & Jacobians

A loss function takes millions of inputs, but a derivative can only measure one nudge at a time. A partial derivative does exactly that: freeze every variable except one, wiggle it, record the response — 'the slope along just this axis.'

Do it for every knob, stack the results — and you've built the gradient from the previous lesson. 'Compute the gradient' literally means 'collect every single-knob slope.' Backprop computes them cleverly and all at once, but partial derivatives are what it computes.