Answer
$e^{-x} \cos(x+y)-e^{-x} \sin(x+y)$ and $e^{-x}cos(x+y)$
Work Step by Step
Our aim is to take the first partial derivatives of the given function $f(x,y)$ with respect to $x$, by keeping $y$ as a constant.
$f_x=e^{-x} \cos(x+y)-e^{-x} \sin(x+y)$
Our aim is to take the first partial derivatives of the given function $f(x,y)$ with respect to $y$, by keeping $x$ as a constant.
$f_y=e^{-x}cos(x+y)\times1=e^{-x}cos(x+y)$
