Directions: Find the Taylor series for $\displaystyle f(x)$ centered at the given value of a. [Assume that f has a power series expansion. Do not show that $\displaystyle R_{n}(x)\rightarrow 0.$]

Problem:

$\displaystyle f(x)=\frac{1}{\sqrt{x}}, a=9$

The problem am having, or maybe i am confused, is when i start to list out the derivatives

$\displaystyle f(x)=\frac{1}{\sqrt{x}}$

$\displaystyle f'(x)=-\frac{1}{2}x^{-\frac{3}{2}}$

$\displaystyle f''(x)=\frac{3}{4}x^{-\frac{5}{2}}$

and so on, the functions become difficult to get a value for that i can use to recognize a pattern. I am taking the derivative correctly right? If so can someone help me list the first 3-4 terms of the taylor series?

Thanks