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chain rule

The rule for differentiating a composite function — multiply the outer derivative by the inner derivative.

If y=f(g(x)), then \dfrac{dy}{dx} = f'(g(x))\cdot g'(x) — differentiate the outer function, leaving the inner function alone, then multiply by the derivative of the inner function.

Examples

  • For y=(3x+1)^5: \dfrac{dy}{dx}=5(3x+1)^4\cdot3=15(3x+1)^4.

See also

derivative implicit differentiation
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