1. The problem statement, all variables and given/known data Hi there. The question is: if f(x) is a periodic function with period 2pi and the derivative is f'(x) continuous on [-pi, pi] show that the fourier coefficients of f' are kbk and -kak if the fourier coefficients of f are ak and bk respectively. 2. Relevant equations 3. The attempt at a solution This is my attempt. Doesn't quite get there: so ak' = 1/2pi int from -pi to pi of f'(x) cos kx dx use parts: f'(x) = du f(x) = u cos kx = v -1/k sin kx = dv i get 1/2pi[f(x) cos kx/k + 1/k int from -pi to pi f(x) sin kx] of course the integral in the parts equation is just bk, and the f(x) cos kx/k evaluated from pi to -pi just becomes 2f(pi)cos kpi. So then I'm left with. 1/pi[f(pi)cos k pi + (1/k)bk] I guess I can write it as [(-1)^k f(pi) + (1/k) bk]/pi What did i do wrong??