Chain rule

Calculus · Formula · Appears in 1 lesson

ddxf(g(x))=f′(g(x))⋅g′(x)\frac{d}{dx} f(g(x)) = f'(g(x)) \cdot g'(x)

To differentiate a composition, multiply the outer rate of change by the inner one. Backpropagation is nothing more than this rule applied layer by layer from the loss backwards, reusing each partial result.

Symbols

ff
The outer function.
gg
The inner function.
g′(x)g'(x)
The inner function's own derivative.
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