Note that on the specified interval that converges uniformly on since those points are on the interior of its interval of convergence. Now note that is differentiable to and that by the Weirstrass test or using the ratio/root test that this is uniformly convergent on we can conclude that

Now it is obvious that , so there is part i and for part two repeat a similar process of establishing, uniform convergence of on , uniform convergence of on , and the differentiability of on