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

If f(x)=ln⁡(cos⁡x)f(x)=\ln(\cos x), then f′(x)=f'(x)=

A.1cos⁡x\dfrac{1}{\cos x}
B.tan⁡x\tan x
C.−cos⁡xsin⁡x-\dfrac{\cos x}{\sin x}
D.−tan⁡x-\tan x

Explanation

Core Concept

The chain rule gives 1cos⁡x⋅(−sin⁡x)\frac{1}{\cos x}\cdot(-\sin x). This simplifies to −sin⁡xcos⁡x=−tan⁡x-\frac{\sin x}{\cos x}=-\tan x.

Correct Answer

D−tan⁡x-\tan x

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