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

If f(x)=sin⁡xxf(x)=\dfrac{\sin x}{x}, then f′(x)=f'(x)=

A.xcos⁡x+sin⁡xx2\dfrac{x\cos x+\sin x}{x^2}
B.cos⁡x\cos x
C.xcos⁡x−sin⁡xx\dfrac{x\cos x-\sin x}{x}
D.xcos⁡x−sin⁡xx2\dfrac{x\cos x-\sin x}{x^2}

Explanation

Core Concept

The quotient rule gives xcos⁡x−sin⁡x⋅1x2\dfrac{x\cos x-\sin x\cdot1}{x^2}. So f′(x)=xcos⁡x−sin⁡xx2f'(x)=\dfrac{x\cos x-\sin x}{x^2}.

Correct Answer

Dxcos⁡x−sin⁡xx2\dfrac{x\cos x-\sin x}{x^2}

More Unit 2: Differentiation: Definition and Basic Derivative Rules practice questions

Try a random question →

Practice more AP Calculus AB questions with full explanations

Practice Unit 2: Differentiation: Definition and Basic Derivative Rules Questions →