Suppose f:R-->R satisfies f(xy) = xf(y)+yf(x) for all real numbers x,y. Prove that f(1)=0 and that f(u^n)=n*u^(n-1)*f(u) for all natural numbers n and all real numbers u.

I really have no clue where to start on this proof, except that the hint in the problem says that in using induction on n, consider the case u = 0 separately.

Any help would be much appreciated.