Hi, I have a function f(x,y). u = ax + by and v = bx - ay. a and b are constants. i need to prove that d2f/du2 + d2f/dv2 = 0.

I have started out by finding df/du using chain rule:

df/du = df/dx * dx/du + df/dy * dy/du

Hence, df/du = df/a*dx + df/b*dy

My problem is that now i need to find d^2f/du^2 but i do not know how to continue from df/du (ie. i do not know how i can differentiate df/a*dx + df/b*dy with respect to u).

Thanks for reading