Using differentiation to find a power series representation of the following function

Question

The problem that was given was to use differentiation to find a power series representation of the following function $\frac{1}{(x+6)^2}$. I know how to find the power series representations of something like $\frac{1}{1-x}$ but the power of $2$ is throwing me off. I assume I have to differentiate the function first then what?

You need to find the first few derivatives to see a patren based on it you can write down a formula for the $n$th derivative. — Mhenni Benghorbal, Nov 24 '13 at 15:30

score 1 · Answer 1 · answered Nov 24 '13 at 15:25

1

HINT:

You know $\displaystyle(1-x)^{-1}=1+x+x^2+\cdots$ if $|x|\le1$

Set $x=-y\implies\cdots$

Now differentiate either sides wrt $y$ as we know $\displaystyle\frac{d (1+x)^{-1}}{dx}=-\frac1{(1+x)^2}$

answered Nov 24 '13 at 15:25

lab bhattacharjee

274,582

Using differentiation to find a power series representation of the following function

1 Answers1