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Thread: Limits and the Power Rule

  1. #1
    Junior Member
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    Jul 2009
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    Limits and the Power Rule

    I did this one using the Power Rule

    $\displaystyle
    f(x)=\frac{(x^10-x^2)}{x^3}
    $

    And I Get

    $\displaystyle
    \frac{10x^9-2x}{3x^2}
    $

    $\displaystyle
    \frac{10x^8-2}{3x}
    $

    $\displaystyle
    \frac{2(5x^8-1)}{3x}
    $

    I'm supposed to find the derivative. Is that it to this?
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  2. #2
    Super Member
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    $\displaystyle
    f(x)=\frac{(x^10-x^2)}{x^3}
    $

    Should this be:

    $\displaystyle
    F(x)=\frac{x^{10}-x^2}{x^3}
    $

    We are actually using the quotient rule here (which is really the power rule, and implicit differentiation but whatever):

    $\displaystyle F'(x)=\frac{[f'(x)][g(x)]-[f(x)][g'(x)]}{[g(x)]^2}$

    In this equation

    $\displaystyle f(x)=(x^{10}-x^2)$
    $\displaystyle g(x)=x^3$
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