Answer
$F_x=\cos{(e^x)}$, $F_y=-\cos{(e^y)}$.
Work Step by Step
$F(x,y)=\int_y^x\cos{(e^t)}dt$
In order to find $F_x$ we treat $y$ as a constant and differentiate with respect to $x$.
$F_x=\cos{(e^x)}$
In order to find $F_y$ we treat $x$ as a constant and differentiate with respect to $y$.
$F_y=-\cos{(e^y)}$
