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Homework Help: Find derivative using Quotient rule

  1. Oct 5, 2008 #1
    1. The problem statement, all variables and given/known data
    Differentiate

    f(x) = 6-5x-x2 / x2-1
    -------
    A) -5-5x / x2-1

    B) 5 / (x+1)2

    C) -5-5x / (x2-1)2

    D) -5 / (x+1)2

    E) -5+5x / x2-1

    F) None of the above

    3. The attempt at a solution
    (x2)(-5-2x)-(6-5x-x2)(2x) / (x2-1)2

    Simplified to:

    5x2-10x+5 / x4-2x2+1

    But it's not one of the answer choices. I tried simplifying it even further to:

    5(x2-2x) / x4-2x2+1
    or
    5(x2-2x) / (x2-1)2

    But I can't see where else to go with it.
     
  2. jcsd
  3. Oct 5, 2008 #2
    Ok so you're taking a quiz or exam? So I think it's best to wait till you're done :)
     
  4. Oct 5, 2008 #3
    It actually is just homework
     
  5. Oct 5, 2008 #4
    I don't see much hw with multiple choice, so yeah ...
     
  6. Oct 5, 2008 #5
    I don't even get the benefit of the doubt? I can guarantee you that this is just a homework problem.

    But if you're not going to believe or help me, can you at least tell me if I'm headed in the right direction or did I miss something?
     
  7. Oct 5, 2008 #6
    "(x^2)(-5-2x)-(6-5x-x^2)(2x) / (x2-1)^2"

    the first (x^2) should be (x^2 - 1)

    it could also be possible that the answers you are given are in a simplified form. What are the answers?
     
  8. Oct 5, 2008 #7
    These are the choices:

    (A) -5-5x / x2-1

    (B) 5 / (x+1)2

    (C) -5-5x / (x2-1)2

    (D) -5 / (x+1)2

    (E) -5+5x / x2-1

    (F) None of the above

    -------------

    Yea, I forgot to put the "-1", but I did do it on my paper.

    From:
    (x2-1)(-5-2x)-(6-5x-x2)(2x) / (x2-1)2

    I got:
    -5x2+5-2x3+2x-12x+10x2+2x3 / x4-2x2+1

    Simplified to:
    5x2-10x+5 / x4-2x2+1

    to

    5(x2-2x+1) / (x2-1)2
    or
    5(x-1)2 / (x2-1)2

    But I don't know where to go from there
     
  9. Oct 5, 2008 #8
    5(x-1)2 / (x2-1)2 is correct thusfar. Just notice that (x2-1) is a difference of two squares. Change it to (x+1)(x-1) and your answer simplifies to (B), which should be correct.
     
    Last edited: Oct 5, 2008
  10. Oct 5, 2008 #9
    I completely missed that. Thanks!
     
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