Partial Derivatives & the Gradient · Hard problem

The vector field $\mathbf F = (3x^{2}+5xy,\ x^{2}+3y^{2})$ is NOT the gradient of any function (its components' cross-partials disagree, so it fails Clairaut's test for being conservative). At $x=4$ (for any $y$), find by how much the two cross-partials disagree: $\dfrac{\partial}{\partial y}(3x^2+5xy) - \dfrac{\partial}{\partial x}(x^2+3y^2)$.