I have an engineering application, that amounts to a differentiation problem that has me stumped.

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?