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Differentiating Inverse Trig Functions

AP Calculus AB· difficulty 3/5

ddxarcsin⁡(x2)=\dfrac{d}{dx}\arcsin(x^2) =

  • A

    2x1−x2\dfrac{2x}{\sqrt{1-x^2}}

  • B

    2x1−x4\dfrac{2x}{\sqrt{1-x^4}}

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  • C

    11−x4\dfrac{1}{\sqrt{1-x^4}}

  • D

    11−x2\dfrac{1}{\sqrt{1-x^2}}

Explanation

11−(x2)2⋅2x=2x1−x4\dfrac{1}{\sqrt{1-(x^2)^2}} \cdot 2x = \dfrac{2x}{\sqrt{1-x^4}}.

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