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Chain Rule

  1. May 23, 2009 #1
    1. The problem statement, all variables and given/known data

    I am supposed to find the derivative of: x(3-x^2)^-2

    2. Relevant equations

    The chain rule

    3. The attempt at a solution

    Well I feel that I am good at using the chain rule but something tells me I can't use it here, because when I do, I only get about half of the answer.

    But anyway, I multiplied x by -2 , which I multiplied by the group (3-x^2)^-3. Then I multiplied that term by the derivative of the first group, (3-x^2), and got: 4x^2 * (3-x^-2)^-3

    however, the right answer is listed as: 4x^2 *(3-x^2)^-3 + (3-x^2)^-2

    for some reason I don't think the chain rule applies to this problem? or perhaps I am doing it wrong... I would appreciate any help or explanation
  2. jcsd
  3. May 24, 2009 #2


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    Homework Helper

    Use the product rule ;-) (or quotient rule, if you prefer) It generates two terms, but you only found one of them.
  4. May 24, 2009 #3
    Like diazona says, the product rule (combined with your chain rule) shall set you free! :smile:

    If it was simply


    then the chain rule would have sufficed.

    However, you have two terms involving x that are multiplied with each other so you also need to incorporate the product rule (or quotient rule for this particular case, but I'd personally prefer the product rule).
  5. May 24, 2009 #4
    Thank you very much guys! I see where I went wrong. I appreciate your help, thanks again :)
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