The chain rule

When one function feeds another, rates of change multiply. If y changes 3 times as fast as u, and u changes 2 times as fast as x, then y changes 3 × 2 = 6 times as fast as x. That is the chain rule. For y = (2x)², the outer rate is 2 × (2x) and the inner rate is 2, so dy/dx = 8x.

Why it matters: A neural network is a long chain of functions; backpropagation is the chain rule applied layer by layer.

Builds on: Slope and the derivative

Learn it, then prove it

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