Answer
$w_{xy}=w_{yx}=\dfrac{1}{y}+\dfrac{1}{x} $
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:
$w_x=e^x+\ln y+\dfrac{y}{x} \\w_y=\dfrac{x}{y}+\ln(x)$
The second partial derivatives are:
$w_{xy}=\dfrac{1}{y}+\dfrac{1}{x} \\w_{yx}=\dfrac{1}{y}+\dfrac{1}{x} $
