1. The problem statement, all variables and given/known data f(t)=t*e^(-2t^2) Find the Fourier Transform F(w) of f(t). It is given that when f(t)=e^[(-at^2)/2] F(w)=√(2*pi/a)*e^[(-w^2)/2a] 2. Relevant equations 3. The attempt at a solution The transform of e^(-2t^2) is easily obtained from the given information, and I got stuck when I tried to do it with integrate by part. Is it related to the convolution? something like F(fg)=F(f)F(g) ?? Is there any theorem for the Fourier Transform of t*f(t)? And also for Laplace Transform too?