# How do you find the partial derivative of f(x,y) = xe^y + ye^x?

May 13, 2015

First, you must bear in mind the rules for deriving $e$: the derived form of ${e}^{f} \left(x\right)$ is $f \left(x\right) {e}^{f} \left(x\right)$.

The partial derivative for $x$ is:

${e}^{y}$ + $y . {e}^{x} .1$

(note that the number 1 here refers to deriving the $x$ in the second element of the function - no need to put that in your answer, it's jut to clear things out)

The partial derivative for $y$ is:

$x . {e}^{y} .1$ + ${e}^{x}$

Same logic here :)