The problem involves finding the 100th derivative of the function f(x) = x/(1+x^2) at the point x=1. The context is centered around derivatives and power series representation.
Multiple approaches are being explored, including power series and partial fraction decomposition. Some participants are questioning the assumptions about the behavior of derivatives at the specified point, and hints have been offered to consider alternative methods.
There is mention of the function being a fraction and the potential complexity of derivatives at x=1. The discussion reflects uncertainty about the convergence of series and the implications of using partial fractions.
Count Iblis said:Fleem, it is a fraction.
Hint: split it in partial fractions.
eok20 said: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?