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Math Help - finishing a quotient rule problem

  1. #1
    Newbie
    Joined
    Jul 2010
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    23

    finishing a quotient rule problem

    the function is x/(square root(x-1)) . find the derivative with respect to x

    so i have this so far;

    ((x-1)^(1/2) - (X)(1/2)(x-1)^(-1/2))/(x-1)^(3/2)

    im stuck for the next steps
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  2. #2
    MHF Contributor
    Joined
    Apr 2008
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    1,092
    Hi Nando, your first step is not quite correct. The denominator should just be x - 1, not (x - 1)^{3/2}. You might want to consider writing the original function as \frac{x}{\sqrt{x - 1}} = \frac{x - 1 + 1}{\sqrt{x - 1}} = \frac{x - 1}{\sqrt{x - 1}} + \frac{1}{\sqrt{x - 1}} = \sqrt{x - 1} + \frac{1}{\sqrt{x - 1}}. This way you can take the derivative easily without having to use the quotient rule.
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