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Math Help - Help with differentiation.

  1. #1
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    Help with differentiation.

    dy/dx of :

    y=cos(x) / (e^x) +1

    __________________________________________

    This is what I have got so far:

    Use the quotient rule, so make u=cos(x) and make v=(e^x)+1

    y=u/v

    dy/dx = [(e^x)+1 * -sin(x) - cos(x) * e^x ] / ((e^x)+1)^2

    What do I do next?
    Last edited by mr fantastic; July 12th 2010 at 07:37 PM. Reason: Deleted excessive ?'s in post title.
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  2. #2
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    looks like you got it.
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  3. #3
    A Plied Mathematician
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    Use some more parentheses, though! Parentheses make things clearer.
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  4. #4
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    a different approach

    You did the quotient rule just fine, but I often avoid it if I'm not required to use it. Any quotient rule problem I've ever encountered can become a product rule + chain rule problem. Consider the following:

    y=\frac{\cos(x)}{e^x+1}=\cos(x)(e^x+1)^{-1}

    Then,

    \frac{dy}{dx}=-\sin(x)(e^x+1)^{-1}+\cos(x)(-1)(e^x+1)^{-2}(e^x)

    =(e^x+1)^{-2}[(e^x+1)(-\sin(x))-(e^x)(\cos(x))]

    =\frac{(e^x+1)(-\sin(x))-(e^x)(\cos(x))}{(e^x+1)^2}

    Much easier in my opinion, and you get the same answer.
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