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?

You don't need to find $f(x)$. To do part (b), you only need to think about the coefficients of the Taylor series of $f(x)$ at $x=3$.
