7. For a polynomial p of degree < n, prove that n n )k p(k), p(k) (0)_xk+1 = (1)* - (k+1)! k=0 k=0 )(x) -xk+1, (k+1)!' where p(k) is the k-th derivative of p. Hint: Reduce the problem to p(x) = x for 0 j n.