Answer
$y^2$
Work Step by Step
Here, we have $f(x, y)=4x^3y$ and $g (x, y)=xy^2+x^4$
The curl $F$ can be calculated as:
$\dfrac{\partial g}{\partial x}-\dfrac{\partial f}{\partial x}=\dfrac{\partial }{\partial x}[xy^2+x^4]-\dfrac{\partial}{\partial y}[4x^3y]$
or, $=y^2+4x^3-4x^3$
or, $=y^2$
