Answer
$w_{xy}=w_{yx}=1/y+1/x$
Work Step by Step
Take the first partial derivatives of the given function. When taking partial derivative with respect to x, treat y as a constant, and vice versa:
$w_x=e^x+\ln y+\frac{y}{x}$
$w_y=\frac{x}{y}+\ln x$
Then take the derivative of the first order partial derivatives to find second partial derivatives with respect to $x$ and $y$:
$w_{xy}=1/y+1/x$
$w_{yx}=1/y+1/x$
