The Chain Rule & Implicit Differentiation · Superchallenge problem

A smooth function $f(x,y)$ satisfies $f_{xx} + f_{yy} = x$ everywhere. Let $g(u,v) = f(u^2 - v^2,\ 2uv)$. Find $g_{uu} + g_{vv}$ at $(u,v) = (2, 1)$.