I ask for help on this math problem that was among my exercises and that I can't seem to get done properly :steam: even if it's tagged as easy

given the function f = x f( x/y )

prove that every tangent plane passes through the point (0,0,0)

now I know that I just have to use the equation of the tangent plane, which in 2 variables is z-z(0) = f'(x) (x-x(0)) + f'(y) (y - y(0))

and then substiute 0 0 0 for z0 x0 y0

yet I don't seem to get the derivative right, probably, because I can't prove the equality right