Calculus Derivatives, OMG!!!

That's it! I'm so damn frusterated I... I.. AHHH!!

So, it's 2:07am and I work in afew hours. I just finished my derivatives exam through online school and I got 100%. But that's not the point, the point is that there are still some questions that are ........ing me off. For instance:

The book says:

"Find the second derivative of: ((x^2)+1)^(1/2)"

Okay, "Simple", I think. I found the first derivative to be:

x((x^2)+1)^(-1/2)

The book agrees with that answer, except for the second derivative. The book believes that the second derivative is ((x^2)+1)^(-3/2) which makes no sense at all. How is this possible? I tried using the Product Rule w/ Chain Rule which would normally go like this:

X = V

((x^2)+1)^(-1/2) = U

V ' = Derivative of V

U ' = Derivative of U

So now, my derivative should be:

(V ')(U) + (U ')(V) = 0

Which is quite long for me to type out, but anyways, I end up with an answer which should include X^2, but it doesn't. I'm frusterated, this makes no sense. Please help.