For a composite function

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

For a composite function y=f(g(x))y=f(g(x)), which of the following gives dydx\dfrac{dy}{dx}? (a) f′(x) g(x)f'(x)\,g(x) (b) f(g(x)) g′(x)f(g(x))\,g'(x) (c) f′(g(x)) g′(x)f'(g(x))\,g'(x) (d) f′(x) g′(x)f'(x)\,g'(x)

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