5The chain rule dh(g(x))∕dx = h′(g(x))g′(x ) gives that f(2)′(x∗3) = df(f(x∗3))∕dx = f ′(f(x∗3))f′(x∗3) = f′(x∗4)f′(x∗3) and similarly for f(2)′(x∗4) . We can prove by induction that for the n solutions x∗n+1,x∗n+2,...,x∗2n that belong to the n -cycle of the equation x = f(n)(x) we have that f(n)′(xn+i) = f′(xn+1) f′(xn+2)...f′(x2n) for every i = 1,...,n .