Why are you struggling with these? It's just a bunch of constants. Break out you Chain Rule and give it a go.
\(\displaystyle f(t)\,=\,(1-\beta*t)^{-\alpha}\)
\(\displaystyle \frac{df}{dt}\,=\,-\alpha*(1-\beta*t)^{-\alpha-1}*(-\beta)\,=\,\alpha\beta*(1-\beta*t)^{-(\alpha+1)}\)
You do the other one and show us what you get.