Deriving MGF for binomial distribution Using the definition of the binomial distribution, I obtain that:
$$\Psi (t) = (pe^t+q)^n $$
I then compute $\Psi ' = npe^t(pe^t+q)^{n-1}$
I then evaluated this at $\Psi'(0)$ and got $\Psi'(0)=np(p+q)^{n-1}$
and so $E[X]$ which I know is $np$. 
How do I then differentiate $\Psi'(t)$ again, the $n-1$ is throwing me off?

Put p+q=1( by property of binomial distribution), and you get E(X)=np
