Apentix/AP Calculus AB/Unit 2: Differentiation: Definition and Basic Derivative Rules/Question
AP Calculus ABhardmcq1 pt

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

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

Explanation

Core Concept

The product rule gives cos⁡x⋅cos⁡x+sin⁡x⋅(−sin⁡x)=cos⁡2x−sin⁡2x\cos x\cdot\cos x+\sin x\cdot(-\sin x)=\cos^2 x-\sin^2 x. The derivative of cos⁡x\cos x supplies the minus sign.

Correct Answer

Acos⁡2x−sin⁡2x\cos^2 x-\sin^2 x

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