If where both and are differentiable

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

Problem

y=f(g(x))

where both

f

and

g

are differentiable, which of the following expressions correctly gives

\dfrac{dy}{dx}

in terms of

f

and

g

? (a)

f'(x)\,g'(x)

(b)

f'(g(x))\,g'(x)

(c)

f'(g(x))+g'(x)

(d)

g'(f(x))\,f'(x)

Related theory

Advanced Differentiation
Differentiation Rules
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability

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