The Exponential Function (e) find dy/dx

**BCHurricane89** · January 26th 2009, 02:06 PM

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

**Chris L T521** · January 26th 2009, 02:24 PM

Originally Posted by BCHurricane89

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

**BCHurricane89** · January 26th 2009, 02:57 PM

Sweet, got it, thanks!

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