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Question $13$ of $13$

Find a power series for $f(x)=\frac{4x}{(x^{2}1{)}^2},|x|<mn>1</mn>$ in the form ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n.$

Hint: First, find the power series for $g(x)=(1x^2{)}^{-1}$ and then differentiate.

$($Express numbers in exact form. Use symbolic notation and fractions where needed.$)$

$a_n=$