Calculus
Intermediate

Chain Rule

Derivative of a composite function.

Formula

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

Variables

f, gFunctions

Example

d/dx (3x+1)⁵ = 5(3x+1)⁴ · 3 = 15(3x+1)⁴.

Did You Know?

The chain rule is what lets you differentiate functions inside functions — the engine behind neural-network training today.

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