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

If f(x)=cos⁡xx2f(x)=\dfrac{\cos x}{x^2}, then f′(x)=f'(x)=

A.xsin⁡x+2cos⁡xx3\dfrac{x\sin x+2\cos x}{x^3}
B.−sin⁡x2x\dfrac{-\sin x}{2x}
C.−xsin⁡x+2cos⁡xx4-\dfrac{x\sin x+2\cos x}{x^4}
D.−xsin⁡x+2cos⁡xx3-\dfrac{x\sin x+2\cos x}{x^3}

Explanation

Core Concept

The quotient rule gives −x2sin⁡x−2xcos⁡xx4\dfrac{-x^2\sin x-2x\cos x}{x^4}. Canceling one factor of xx gives −xsin⁡x+2cos⁡xx3-\dfrac{x\sin x+2\cos x}{x^3}.

Correct Answer

D−xsin⁡x+2cos⁡xx3-\dfrac{x\sin x+2\cos x}{x^3}

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