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Applying the Power Rule

AP Calculus AB· difficulty 2/5

If f(x)=x−1/3f(x) = x^{-1/3}, then f′(x)=f'(x) =

  • A

    −13x−4/3-\tfrac{1}{3}x^{-4/3}

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  • B

    −3x−4/3-3 x^{-4/3}

  • C

    13x−2/3\tfrac{1}{3}x^{-2/3}

  • D

    3x−2/33x^{-2/3}

Explanation

Power rule: −1/3⋅x−1/3−1=−13x−4/3-1/3 \cdot x^{-1/3 - 1} = -\tfrac{1}{3} x^{-4/3}.

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