The equations,

$\displaystyle x^{3} + xy - uy = v + 4,$ $\displaystyle y^{2} - xy^{3} + uv = 1,$

define x and y as functions of u and v. Find,$\displaystyle \frac{\partial{x}}{\partial{v}}

$

See figure attached for my attempt. It get's a little messy with the bottom determinant, so I'm not entirely convinced I've done this correctly.

Did I do anything wrong?