Given function and given differential of the function - how do I get there?

Hey mathematicians,

I have looked at this for quite some time...

I have (which is given)

f(x) = 2*x^2 / (x^4 +1)

and I have (which is also given)

f ' (x) = ( 4x (1 + x^2) (1+x) (1-x) ) / (x^4 + 1)^2

... So, I'm looking to find the steps to get to the given f ' (x)...

I have already worked quite a lot on it, but what i end getting is this...

I won't get into the (x^4 + 1)^2-part - as it is quite simple, but I get...

- 4x^5 + 4x => -4x (x^4 - 1)

Okay, so how do I get the last expression into factors?

What bothers me is the minus in front of 4x..? How do I get rid of it?

I hope someone has the time to help me out... It would be much appreciated.

Yours sincerely, Simon, DK.