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Math Help - Derivative of a fraction

  1. #1
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    Derivative of a fraction

    I 've been trying to find the derivative of this function and it's a little confusing.

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

    I started out by using the quotient rule getting:

     f^l(x)= \frac{(9x^2-2x)(x^\frac{1}{2})-[(3x^3-x^2+2)(\frac{1}{2}x^\frac{-1}{2})]}{x^\frac{1}{4}}

    Then multiplying this out and combining like terms:

     f^l(x)= \frac{\frac{15}{2}x^\frac{5}{2}-\frac{3}{2}x^\frac{3}{2}+x^\frac{-1}{2}}{x^\frac{1}{4}}

    The final solution is  f^l(x)= \frac{15}{2}x^\frac{3}{2}-\frac{3}{2}x^\frac{1}{2}-x^\frac{-3}{2}

    I just cant seem to get from the last step to the solution. Can anyone help? Thanks
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  2. #2
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     f^l(x)= \frac{(9x^2-2x)(x^\frac{1}{2})-[(3x^3-x^2+2)(\frac{1}{2}x^\frac{-1}{2})]}{(x^\frac{1}{2})^2}
     f^l(x)= \frac{(9x^2-2x)(x^\frac{1}{2})-[(3x^3-x^2+2)(\frac{1}{2}x^\frac{-1}{2})]}{x}
     f^l(x)= \frac{\frac{15}{2}x^\frac{5}{2}-\frac{3}{2}x^\frac{3}{2}+x^\frac{-1}{2}}{x}
     \\  f^l(x)= \frac{15}{2}x^\frac{3}{2}-\frac{3}{2}x^\frac{1}{2}-x^\frac{-3}{2}
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