Calculus
posted by W .
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!

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
...
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