help with partial derivative of e^(xe^y) in tems of y

Dec 2008
24
0
I have to find Fy of e^(xe^y) .. Fx is no problem but I can't seem to figure out how to take the partial derivative in terms of y of e^(xe^y) ... the syntax of the two exponential functions is really confusing me.

Thanks,
Jeff
 

Ackbeet

MHF Hall of Honor
Jun 2010
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There's actually less there than meets the eye. Use the chain rule a few times to get your result.
 
Jun 2009
696
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United States
\(\displaystyle f(x,y)=e^{xe^y}\)

To differentiate with respect to y, just remember to use the chain rule.

\(\displaystyle \frac{\partial f}{\partial y}=\left(\frac{\partial}{\partial y}xe^y}\right)e^{xe^y} \)