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

If f(x)=xsin⁡xf(x)=x\sin x, then f′′(x)=f''(x)=

A.2cos⁡x−xsin⁡x2\cos x-x\sin x
B.sin⁡x+xcos⁡x\sin x+x\cos x
C.2cos⁡x+xsin⁡x2\cos x+x\sin x
D.cos⁡x\cos x

Explanation

Core Concept

The product rule gives f′(x)=sin⁡x+xcos⁡xf'(x)=\sin x+x\cos x. Differentiating again gives cos⁡x+cos⁡x−xsin⁡x=2cos⁡x−xsin⁡x\cos x+\cos x-x\sin x=2\cos x-x\sin x.

Correct Answer

A2cos⁡x−xsin⁡x2\cos x-x\sin x

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