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Going from First to Second Derivative

I have a first derivative and a second derivative, how do you get from the first to the second, I can't solve it.

Please see the attached file for the fully formatted problems.

M'(t) = pe^t/(1 - t^tq)^2
M''(t) = pe^t(1 + qe^t)/(1 - (e^t)q)^3


Solution Preview

M'(t) = p*exp(t)/[1 - q*exp(t)]^2 = p*f1/f2
M''(t) = p*(f2*f1' - f1*f2')/f2^2
f1 = expt(t) => f1' = ...

Solution Summary

The method of going from a first to a second derivative is shown.