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

If f(x)=arcsin⁡(3x)f(x)=\arcsin(3x), then f′(x)=f'(x)=

A.11−9x2\dfrac{1}{\sqrt{1-9x^2}}
B.31−9x2\dfrac{3}{\sqrt{1-9x^2}}
C.31−3x2\dfrac{3}{\sqrt{1-3x^2}}
D.11−3x2\dfrac{1}{\sqrt{1-3x^2}}

Explanation

Core Concept

Start with 11−(3x)2\frac{1}{\sqrt{1-(3x)^2}}, then multiply by the inner derivative 3. The result is 31−9x2\frac{3}{\sqrt{1-9x^2}}.

Correct Answer

B31−9x2\dfrac{3}{\sqrt{1-9x^2}}

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