Question: Suppose that f(x) is a differentiable periodic function of period 2π. Assume the Fourier series of f is differentiable term by term.
(a) If the Fourier coefficients of f are ak and bk, show that the Fourier coefficients of its derivative f' are kbk and -kak.
(b) How are the amplitudes of the harmonics of f and f' related?
(c) How are the energy spectra of f and f' related?