How to find $f(x)$ in order to find $f^{(10)}(3)$? 
(a) Find the radius of convergence of $\sum_{n=1}^\infty (-1)^n \frac{(x-3)^n}{(2n+1)}$ and its derivative.
(b) Denote by $f(x)$ the function represented by the above power series within its region of convergence. Find $f^{(10)}(3)$, i.e., its 10th derivative at $x = 3$.

I can solve problem (a). However I cannot find f(x). In order to find f(x) how should I do?

Hint: If we have
$$
f(x) = \sum_{n \ge 0} a_n (x-a)^n,
$$
then the $n$th coefficient $a_n$ is also equal to $\frac{f^{(n)}(a)}{n!}$.
