Chapter 11.2, Problem 54E

Differentiating and integrating power series Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series.

44. $g(x)=\frac{x}{{(1+x^2)}^2}$ using $f(x)=\frac{1}{1+x^2}$