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Trouble taking a derivative

  1. Oct 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Derivative of [tex]\frac{y - 1}{y^2 - y + 1}[/tex]

    2. Relevant equations

    3. The attempt at a solution

    The solution is [tex]\frac{y^2 - 2y}{(y^2 - y + 1)^2}[/tex] but in my work, the answer will have something to the 4th power on the top which will be impossible to cancel out. What have I done wrong?

    Edit: Never mind, I see my mistake
    Last edited: Oct 17, 2012
  2. jcsd
  3. Oct 17, 2012 #2
    Remember: [tex]\frac{d}{dx}\frac{f(x)}{g(x)} = \frac{g(x)f'(x) - f(x)g'(x)}{g(x)^2}[/tex]
  4. Oct 17, 2012 #3
    Yes but I don't like to work with the quotient rule. I should be getting the same answer using the product rule anyway, right?

    Edit: Never mind, I see my mistake
  5. Oct 17, 2012 #4
    That's fine.

    Then, remember: [tex]-(y^2-y+1)^{-2} = -\frac{1}{(y^2-y+1)^2}[/tex]
    (An expression to the -2 power doesn't equal 1/sqrt(expression))
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