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Applying the Power Rule

AP Calculus AB· difficulty 2/5

If f(x)=xf(x) = \sqrt{x}, then f′(x)=f'(x) =

  • A

    x/2\sqrt x/2

  • B

    2x2\sqrt x

  • C

    1x\tfrac{1}{\sqrt x}

  • D

    12x\tfrac{1}{2\sqrt x}

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Explanation

x=x1/2\sqrt x = x^{1/2}. f′(x)=12x−1/2=1/(2x)f'(x) = \tfrac{1}{2} x^{-1/2} = 1/(2\sqrt x).

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