Posted by W on .
Write the first four nonzero terms and the general term of the Taylor serires for f about x=0. f(x)=2x/(1+x^2)
I feel that I'm doing this wrong because finding the derivatives of f(x) look really messy. Can you please show me the steps?
Thanks in advance!

Calculus 
Steve,
The derivatives are messy.
f = 2x/(1+x^2)
f' = 2(x^2  1)/(1+x^2)^2
f'' = 4x(x^2  3)/(1+x^2)^3
f''' = 12(x^4  6x^2 + 1)/(1+x^2)^4
...