Analysis of Rational Functions (Using Calculus)

Hi,

So the question is to analyze this rational function... I am easily able to get the first derivative. The second derivative causes my problems though because I don't have the chain rule! My first and most obvious question would be: This isn't an assignment... And we learn the chain rule early this week. Should I just ignore this question until we get the chain rule?

If the answer is no, then here is the first derivative (it is done correctly, as it was an example)

f'(x)= (-5x^2+5)/(x^2+1)^2

I guess, based on theory, that the best form to get this in, would be factored top and bottom. The example goes through one method and I can follow it for quite a while, but then it does one tricky thing that, as far as I can tell, would either be an ambiguous case, or else I don't understand it, so I am asking if someone here could go through the steps how how they would find the second derivative now.

Thanks in advance!

Mike