Apentix/AP Calculus AB/Unit 3: Differentiation: Composite, Implicit, and Inverse Functions/Question
AP Calculus ABmediummcq1 pt

If f(x)=esin⁡xf(x)=e^{\sin x}, then f′(x)=f'(x)=

A.esin⁡xe^{\sin x}
B.ecos⁡xe^{\cos x}
C.cos⁡x esin⁡x\cos x\,e^{\sin x}
D.cos⁡x ecos⁡x\cos x\,e^{\cos x}

Explanation

Core Concept

The derivative of eue^u is eu⋅u′e^u\cdot u'. With u=sin⁡xu=\sin x, this gives esin⁡x⋅cos⁡xe^{\sin x}\cdot\cos x.

Correct Answer

Ccos⁡x esin⁡x\cos x\,e^{\sin x}

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