The Chain Rule & Implicit Differentiation · Challenge problem

The map $u = x^2 - y^2$, $v = 2xy$ is invertible near $(x,y) = (2,1)$, where $(u,v) = (3,4)$. Regard $x$ and $y$ as functions of $u$ and $v$ there. Find $\dfrac{\partial x}{\partial u}$ at $(u,v) = (3,4)$.