Let u = x + y and v = x -y so that x = (u + v)/2 and y = (u-v)/2

Given a twice continuously differentiable functions f(x,y) set

g(u,v) = f( (u+v)/2, (u-v)/2) so that f(x,y) = g( x+y, x-y)

1) Relate ∂f/∂x, ∂f/∂y to ∂g/∂u, ∂g/∂v

2) Relate ∂^2f/∂x^2, ∂^2f/∂y^2 to ∂^2g/∂u^2 , ∂^2g/∂v^2 and ∂^2g/∂u∂v