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Math Help - The Exponential Function (e) find dy/dx

  1. #1
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    The Exponential Function (e) find dy/dx

    \ln xy = e^(x+y) find dy/dx


    thats an e to the x+y also

    I guess im not entirely sure how to go about solving this problem. Do I use the product rule for the lnxy

    Thanks in Advance
    Last edited by BCHurricane89; January 26th 2009 at 03:17 PM.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by BCHurricane89 View Post
    \ln xy = e^(x+y) find dy/dx


    thats an e to the x+y also

    I guess im not entirely sure how to go about solving this problem. Do I use the product rule for the lnxy

    Thanks in Advance
    Note that \ln(xy)=\ln(x)+\ln(y)

    Implicitly differentiating both sides, you should get

    \frac{1}{x}+\frac{1}{y}\frac{\,dy}{\,dx}=\left(1+\  frac{\,dy}{\,dx}\right)e^{x+y}

    Can you solve for \frac{\,dy}{\,dx} now?
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  3. #3
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    Sweet, got it, thanks!
    Last edited by BCHurricane89; January 27th 2009 at 09:59 AM.
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