let f(p,q) be a given function, and let the function F(x,y) be defined by F(x,y)=f(x^2+y^2,2xy).
Show that \({\frac{∂F}{ ∂X}}^{2}+{\frac{∂F}{ ∂Y}}^{2}=4({X}^{2}+{Y}^{2})[{\frac{∂f}{ ∂p}}^{2}+{\frac{∂f}{ ∂q}}^{2}]\)
