Apentix/AP Calculus AB/Unit 3: Differentiation: Composite, Implicit, and Inverse Functions/Question
AP Calculus ABhardmcq1 pt

If f(x)=e2xsin⁡xf(x)=e^{2x}\sin x, then f′′(x)=f''(x)=

A.e2x(2sin⁡x+cos⁡x)e^{2x}(2\sin x+\cos x)
B.e2x(3sin⁡x−4cos⁡x)e^{2x}(3\sin x-4\cos x)
C.e2x(3sin⁡x+4cos⁡x)e^{2x}(3\sin x+4\cos x)
D.e2x(4sin⁡x+3cos⁡x)e^{2x}(4\sin x+3\cos x)

Explanation

Core Concept

First, f′(x)=e2x(2sin⁡x+cos⁡x)f'(x)=e^{2x}(2\sin x+\cos x). Differentiating again gives 2e2x(2sin⁡x+cos⁡x)+e2x(2cos⁡x−sin⁡x)=e2x(3sin⁡x+4cos⁡x)2e^{2x}(2\sin x+\cos x)+e^{2x}(2\cos x-\sin x)=e^{2x}(3\sin x+4\cos x).

Correct Answer

Ce2x(3sin⁡x+4cos⁡x)e^{2x}(3\sin x+4\cos x)

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