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Math Help - Derivative issue

  1. #1
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    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
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  2. #2
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    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''
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  3. #3
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    I got the same 1st derivative, so probably its 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 Im not slipping off...
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  4. #4
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    y'' = \frac{2(x^3-6x^2+3x+1)}{(x^2-x+1)^3}
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