The Chain Rule

AP Calculus AB· difficulty 3/5

ddxx2+13=\dfrac{d}{dx}\sqrt[3]{x^2 + 1} =

  • A

    13(x2+1)2/3\dfrac{1}{3}(x^2+1)^{-2/3}

  • B

    2x3x2+13\dfrac{2x}{3\sqrt[3]{x^2+1}}

  • C

    2x3(x2+1)2/3\dfrac{2x}{3}(x^2+1)^{-2/3}

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  • D

    2x3(x2+1)1/3\dfrac{2x}{3}(x^2+1)^{1/3}

Explanation

(x2+1)1/3(x^2+1)^{1/3}13(x2+1)2/32x=2x3(x2+1)2/3\tfrac{1}{3}(x^2+1)^{-2/3} \cdot 2x = \tfrac{2x}{3(x^2+1)^{2/3}}.

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