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Math Help - Derivative with short cut

  1. #1
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    Derivative with short cut

    Differentiate the following function

    \frac{5x^2+7x+6}{\sqrt{x}}

    =  \frac{10x+7+0}{x^\frac{1}{2}}

    = (x^\frac{-1}{2})(10x+7)

    =  10x^\frac{1}{2}+7x^\frac{-1}{2}

    where am i going wrong?
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  2. #2
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    Quote Originally Posted by silencecloak View Post
    Differentiate the following function

    \frac{5x^2+7x+6}{\sqrt{x}}
    \frac{5x^2 + 7x + 6}{x^{1/2}} = 5x^{3/2} + 7x^{1/2} + 6x^{-1/2}
    Now take the derivative.

    You cannot just take the derivative of numerator and leave the denominator. And you cannot just take the derivative of numerator and denominator at the same time. You need to use the quotient rule, if you learned that. But the best is that do what I did.

    This is Mine 17th Post!!!
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  3. #3
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    so i end up with

     <br /> <br />
\frac{15}{2}x^\frac{1}{2} + \frac{7}{2}x^\frac{-1}{2}-\frac{6}{2}x^\frac{-3}{2}
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  4. #4
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    still wrong :/
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  5. #5
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    Quote Originally Posted by silencecloak View Post
    still wrong :/
    no, it's correct ... maybe some simplification is necessary.
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  6. #6
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    Quote Originally Posted by skeeter View Post
    no, it's correct ... maybe some simplification is necessary.

    well

    this online math homework stuff

    i even simplified the fractions to decimals
    Last edited by ThePerfectHacker; October 1st 2008 at 03:37 PM.
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