Answer
$h_{xx}=0$
$h_{yy}=xe^y$
$h_{xy}=h_{yx}=e^y$
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:
$h_x=e^y$
$h_y=xe^y+1$
Then take the derivative of the first order partial derivatives to find second partial derivatives:
$h_{xx}=0$
$h_{yy}=xe^y$
Second partial derivatives of first order partial derivative of x with respect to y and y with respect to x are the same:
$h_{xy}=h_{yx}=e^y$
