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Math Help - derrivative

  1. #1
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    derrivative

    f(x)=x/[x+(c/x)]

    can you please show all the steps please. Thanks
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  2. #2
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by johntuan View Post
    f(x)=x/[x+(c/x)]

    can you please show all the steps please. Thanks
    Is c a constant? If so

    \frac{x}{x + \frac{c}{x}} = \frac{x}{\frac{x^2+c}{x}}= \frac{x^2}{x^2+c}

    Take the derivative of that

    \frac{(2x)(x^2+c)~-~(2x)(x^2)}{(x^2+c)^2}

    Now just simplify

    \frac{2cx}{(x^2+c)^2}
    Last edited by 11rdc11; October 13th 2008 at 12:25 PM.
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  3. #3
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    You can use the quotient rule, but I don't quite remember it, so I'll just give you the necessary information.
    Top = x
    Derivative of the top= 1
    Bottom = (x + c/x)
    Derivative of the bottom = 1 + -c/(x^2)

    Assuming that c is a constant.
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  4. #4
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    i'm not sure if c is a constant but the answer is f'(x)=2cx/(x^2+c)^2
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