Second moment of negative binomial distribution.

Question

I'm an undergraduate student studying mathematical statistics in Korea. I am trying to get variance of negative binomial distribution by using mgf.

For now, I got first moment of NB.

$ M'(t) = \frac{(1-(1-p)e^t)^r*r(pe^t)^{r-1}*(pe^t-pe^t)^r*r(1-(1-p)e^t)^{r-1}*-(1-p)e^t}{(1-(1-p))^{2r}}$

And I could get mean $\frac{r}{p}$ by inserting 0

But the moment I try to get second moment, I don't know how to start by using differential method.

But I have to get variance by using second moment, not by using $Var(x)=E[x^2] + E[x]^2$

1. Can you guys differentiate $M'(t)$ one more? just using differential rule? If you can, please show me equations....