Apentix/AP Calculus AB/Unit 3: Differentiation: Composite, Implicit, and Inverse Functions/Question
AP Calculus ABeasymcq1 pt

Which of the following is ddx[arcsin⁡x]\dfrac{d}{dx}\left[\arcsin x\right]?

A.1x2−1\dfrac{1}{\sqrt{x^2-1}}
B.11−x2\dfrac{1}{\sqrt{1-x^2}}
C.−11−x2-\dfrac{1}{\sqrt{1-x^2}}
D.11+x2\dfrac{1}{1+x^2}

Explanation

Core Concept

The derivative of arcsin⁡x\arcsin x is the standard formula 11−x2\frac{1}{\sqrt{1-x^2}}, valid for −1<x<1-1<x<1.

Correct Answer

B11−x2\dfrac{1}{\sqrt{1-x^2}}

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