Let f(t) be an even function, i.e. f(-t) = f(t) for all t. Let the Fourier transform of f(t) be defined as F(ω) = ∫_-∞^∞ f(t)e^-jωtdt for all ω, and suppose F(0) = 1. Then dF(ω) / dω = -ωF(ω) for all ω and F(0)=1.Then