I am trying to find the Fourier Transform of $$f(t) = t^2e^{-t^2}$$ and the teacher gave us the hint to differentiate $e^{-t^2}$ twice, which I did. However, I do not see how that will help me find the transform. I looked up in the soultion sheet where they have done the following,
but I do not see by differentiate $e^{-t^2}$ twice how $t^2e^{-t^2}$ can be equal to that above.