If \(\displaystyle q=\frac{1}{\alpha^2}-(\frac{t}{\alpha}+\frac{1}{\alpha^2})e^{-\alpha t}\)

Find \(\displaystyle \frac{dq}{dt}\).

I came up with \(\displaystyle -\frac{t}{e^{\alpha t}}\) and several other versions, but I know that I'm off.

Can anyone put me on track?