Answer
$w_{xy}=w_{yx}=2y+6xy^2+12x^2y^3$
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:
$w_x=y^2+2xy^3+3x^2y^4 \\w_y=2xy+3x^2y^2+4x^3y^3$
Now, second partial derivatives are:
$w_{xy}=w_{yx}=2y+6xy^2+12x^2y^3$
