Answer
$w_{xy}=w_{yx}=cosy+cosx+1$
Work Step by Step
Take the first partial derivatives of the given function. When taking a partial derivative with respect to x, treat y as a constant, and vice versa:
$w_x=siny+ycosx+y$
$w_y=xcosy+sinx+x$
Then take the derivative of the first order partial derivatives to find second partial derivatives:
$w_{xy}=cosy+cosx+1$
$w_{yx}=cosy+cosx+1$
