# Math Help - Derivative issue

1. ## Derivative issue

Sorry i have posted the similar thread in the college calculus section because i didn't notice that this section exists.I m in a hurry to solve this problem so i made a thread here too.Hope i m right.

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

Find y and y

for the problem i get to
y=(-x^2+4x-1)/(x^2-x+1)^2 by u/v method but the answer of this derivative problem is (Given in the book)
-3(x^2-3x+1)/(x^2-x+1)^3
How can i Get to this form ?
answer is not a typo and this problem is from calculus by howard anton
Thanks

2. y' = (-x^2+4x-1)/(x^2-x+1)^2
your solution for y' is correct

the book solution is incorrect for both y' and y''

3. I got the same 1st derivative, so probably it´s okay.
The 2nd is a pretty ugly one, and after a double and triple check I got:

$\frac{2x^3-12x^2+6x+2}{(x^2-x+1)^3}$
Maybe we need someone else to corroborate this. I hope I´m not slipping off...

4. $y'' = \frac{2(x^3-6x^2+3x+1)}{(x^2-x+1)^3}$