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?

  • $\begingroup$ 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


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 $\displaystyle\frac{d (1+x)^{-1}}{dx}=-\frac1{(1+x)^2}$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.