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

If f(x)=arcsin⁡(x2)f(x)=\arcsin(x^2), then f′(x)=f'(x)=

A.11−x4\dfrac{1}{\sqrt{1-x^4}}
B.2x1−x4\dfrac{2x}{1-x^4}
C.2x1−x2\dfrac{2x}{\sqrt{1-x^2}}
D.2x1−x4\dfrac{2x}{\sqrt{1-x^4}}

Explanation

Core Concept

Start with 11−(x2)2\frac{1}{\sqrt{1-(x^2)^2}}, then multiply by the inner derivative 2x2x. The result is 2x1−x4\frac{2x}{\sqrt{1-x^4}}.

Correct Answer

D2x1−x4\dfrac{2x}{\sqrt{1-x^4}}

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