Answer
$f_{xx}=24x$
$f_{yy}=-2x$
$f_{xy}=f_{yx}=-2y$
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:
$f_{x}=12x^2-y^2$
$f_{y}=-2xy$
Then take the derivative of the first order partial derivatives to find second partial derivatives:
$f_{xx}=24x$
$f_{yy}=-2x$
Second partial derivatives of first order partial derivative of x with respect to y and y with respect to x are the same:
$f_{xy}=f_{yx}=-2y$
