Apentix/AP Calculus AB/Unit 2: Differentiation: Definition and Basic Derivative Rules/Question
AP Calculus ABeasymcq1 pt

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

A.xcos⁡xx\cos x
B.sin⁡x+cos⁡x\sin x+\cos x
C.cos⁡x\cos x
D.sin⁡x+xcos⁡x\sin x+x\cos x

Explanation

Core Concept

The product rule gives 1⋅sin⁡x+x⋅cos⁡x=sin⁡x+xcos⁡x1\cdot\sin x+x\cdot\cos x=\sin x+x\cos x. Each factor is differentiated in turn.

Correct Answer

Dsin⁡x+xcos⁡x\sin x+x\cos x

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