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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 -

    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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