# 100th derivative

1. Aug 2, 2009

### eok20

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. Aug 2, 2009

### fleem

Maybe i'm missing something but since this is a second-order equation, aren't all derivatives past the second one zero?

3. Aug 2, 2009

### Count Iblis

Fleem, it is a fraction.

Hint: split it in partial fractions.

4. Aug 2, 2009

### fleem

I need glasses.

5. Aug 2, 2009

### John Creighto

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