Suppose f: R -> R is differentiable and let h(x,y) = f(√(x^2 + y^2)) for x ≠ 0. Letting r = √(x^2 + y^2), show that:

x(dh/dx) + y(dh/dy) = rf'(r).

I have begun by showing that rf'(r) = sqrt(x^2 + y^2) * lim_{t->0}(f(r+t) - f(r))/t

and written out the definition form of the directional derivatives. I cant seem to find a way to equate both sides of the equation. Can anyone help?