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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?

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  • $\begingroup$ 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. $\endgroup$ – Mhenni Benghorbal Nov 24 '13 at 15:30
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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 $\displaystyle\frac{d (1+x)^{-1}}{dx}=-\frac1{(1+x)^2}$

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