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Math Help - Applying the power rule to problems

  1. #1
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    Applying the power rule to problems



    How exactly would one go about using the power rule to solve this problem?
    I'm trying to find the best method, in preparation for a test this week.
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  2. #2
    Senior Member Pinkk's Avatar
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    The power rule: \frac{d}{dx}x^{n}=nx^{n-1}

    a) f(x)=2x^{2}+3x-x^{-1}

    Using the power rule:

    f'(x)=(2)(2)x^{2-1}+(1)(3)x^{1-1}-(-1)x^{-1-1}

    f'(x)=4x+3+\frac{1}{x^{2}}

    b) f(x)=x+x^{-\frac{1}{2}}

    Using the power rule:

    f'(x)=(1)x^{1-1}+(-\frac{1}{2})x^{-\frac{3}{2}}

    f'(x)=1-\frac{1}{2\sqrt{x^{3}}}
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