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100th derivative

  1. Aug 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the 100th derivative at 1 of f(x) = x/(1+x^2)


    2. Relevant equations



    3. The attempt at a solution
    For |x| < 1 I can write f as a power series (since 1/(1+x^2) = sum_n (-1)^n x^(2n)) but this won't work at 1. I tried writing out the first few derivatives at 1 explicitly but things got pretty messy. Any ideas?
     
  2. jcsd
  3. Aug 2, 2009 #2
    Maybe i'm missing something but since this is a second-order equation, aren't all derivatives past the second one zero?
     
  4. Aug 2, 2009 #3
    Fleem, it is a fraction.

    Hint: split it in partial fractions.
     
  5. Aug 2, 2009 #4
    I need glasses.
     
  6. Aug 2, 2009 #5
    Are you just trying to find the derivative at one point? If so, and you are trying to find the derivative at the point x=1, then why not do the power series at about x=1. If you use partial fractions as another poster suggested, the roots will be +/=i so I think the series should converge
     
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