Given $\displaystyle f(x) = \frac{1}{3+2x}$ and $a = 3$, find $f'(x)$, $f''(x)$, $f'''(x)$, $f''''(x)$, then for general $n$.

a. Find the formula for $f^{(n)}(x)$ and simplify.

b. Find $f^{(n)}(3)$ and simplify.

c. Find the Taylor coefficient $\displaystyle C\_n = \frac{1}{n!}f^{(n)}(3)$ and simplify.

I got part a correct but apparently parts b and c are incorrect? Can someone tell me what I'm doing wrong?
[![enter image description here](https://i.stack.imgur.com/DQuV1.jpg)](https://i.stack.imgur.com/DQuV1.jpg)