Answer
$f_{xx}(x,y)=24x$
$f_{xy}(x,y)=-2y$
$f_{yx}(x,y)=-2y$
$f_{yy}(x,y)=-2x$
Work Step by Step
Given: $f(x,y)=4x^3-xy^2$
Partial differentiate with respect to $x$ is $f_x= 12x^2-y^2$ ...(1)
Partial differentiate equation (1) with respect to $x$ is $f_{xx}(x,y)=24x$
Partial differentiate equation (1) with respect to $y$ is$f_{xy}(x,y)=-2y$
Partial differentiate with respect to $y$ is $f_x=-2xy$ .... (2)
Partial differentiate equation (2) with respect to $x$ is $f_{yx}(x,y)=-2y$
Partial differentiate equation (2) with respect to $y$ is $f_{yy}(x,y)=-2x$
