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

If f(x)=arccos⁡(ex)f(x)=\arccos(e^x), then f′(x)=f'(x)=

A.−ex1−ex-\dfrac{e^x}{\sqrt{1-e^x}}
B.−ex1−e2x-\dfrac{e^x}{\sqrt{1-e^{2x}}}
C.ex1−e2x\dfrac{e^x}{\sqrt{1-e^{2x}}}
D.−11−e2x-\dfrac{1}{\sqrt{1-e^{2x}}}

Explanation

Core Concept

Start with −11−(ex)2-\frac{1}{\sqrt{1-(e^x)^2}}, then multiply by the inner derivative exe^x. The result is −ex1−e2x-\frac{e^x}{\sqrt{1-e^{2x}}}.

Correct Answer

B−ex1−e2x-\dfrac{e^x}{\sqrt{1-e^{2x}}}

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