Apentix/AP Calculus AB/Unit 3: Differentiation: Composite, Implicit, and Inverse Functions/Question
AP Calculus ABmediummcq1 pt

If f(x)=e2xcos⁡xf(x)=e^{2x}\cos x, then f′(x)=f'(x)=

A.2e2xcos⁡x+e2xsin⁡x2e^{2x}\cos x+e^{2x}\sin x
B.−2e2xsin⁡x-2e^{2x}\sin x
C.2e2xcos⁡x2e^{2x}\cos x
D.2e2xcos⁡x−e2xsin⁡x2e^{2x}\cos x-e^{2x}\sin x

Explanation

Core Concept

Use the product rule with the chain rule on the first factor. The result is 2e2xcos⁡x+e2x(−sin⁡x)2e^{2x}\cos x+e^{2x}(-\sin x).

Correct Answer

D2e2xcos⁡x−e2xsin⁡x2e^{2x}\cos x-e^{2x}\sin x

More Unit 3: Differentiation: Composite, Implicit, and Inverse Functions practice questions

Try a random question →

Practice more AP Calculus AB questions with full explanations

Practice Unit 3: Differentiation: Composite, Implicit, and Inverse Functions Questions →