How to prove connection between two functions

Question

Let $F$ be a two-variable function, namely $F(u,v)$.

If $F''_{uu} + F''_{vv} = 0$ and $G(x,y)= F((x^2+y^2)/2, xy)$, then how do I prove that $G''_{xx} + G''_{yy} = 0$ ?