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Thread: The Exponential Function (e) find dy/dx

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

    $\displaystyle \ln xy = e^(x+y)$ 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 $\displaystyle lnxy$

    Thanks in Advance
    Last edited by BCHurricane89; Jan 26th 2009 at 02:17 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
    $\displaystyle \ln xy = e^(x+y)$ 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 $\displaystyle lnxy$

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

    Implicitly differentiating both sides, you should get

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

    Can you solve for $\displaystyle \frac{\,dy}{\,dx}$ now?
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  3. #3
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    Sweet, got it, thanks!
    Last edited by BCHurricane89; Jan 27th 2009 at 08:59 AM.
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