-4x (x^4 - 1) = -4x (x^2-1)(x^2+1) - using difference of two squares x^4 and 1
-4x (x^4 - 1) = -4x (x-1)(x+1)(x^2+1) - difference of two squares again x^2 and 1 in this case
-4x (x^4 - 1) = 4x (1-x)(x+1)(x^2+1) - using -(x-1)=(1-x).
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.