Apentix/AP Calculus AB/Unit 2: Differentiation: Definition and Basic Derivative Rules/Question
AP Calculus ABmediummcq1 pt

If f(x)=x2cos⁡xf(x)=x^2\cos x, then f′(x)=f'(x)=

A.2xcos⁡x−x2sin⁡x2x\cos x-x^2\sin x
B.2xcos⁡x+x2sin⁡x2x\cos x+x^2\sin x
C.−2xsin⁡x-2x\sin x
D.x2cos⁡xx^2\cos x

Explanation

Core Concept

The product rule gives 2x⋅cos⁡x+x2⋅(−sin⁡x)=2xcos⁡x−x2sin⁡x2x\cdot\cos x+x^2\cdot(-\sin x)=2x\cos x-x^2\sin x. The derivative of cos⁡x\cos x is −sin⁡x-\sin x.

Correct Answer

A2xcos⁡x−x2sin⁡x2x\cos x-x^2\sin x

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