Answer
$w_{xy}=w_{yx}=\cos y+\cos x+1$
Work Step by Step
Our aim is to take the first partial derivative of the given function $w(x,y)$ with respect to $x$, by treating $y$ as a constant and vice versa:
$w_x=siny+ycosx+y \\w_y=x \space cosy+\sin (x)+x$
Now, find the second partial derivatives.
$w_{xy}=\cos y+\cos x+1 \\w_{yx}=cosy+cosx+1$
