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Quotient rule Differentiation

  1. Jan 19, 2012 #1
    1. The problem statement, all variables and given/known data
    a) Differentiate y=((x-1)/(x+1))^2

    b (non calculus simplification question):
    How would i simplify 10(5x+3)(5x-1)+5(5x-1)^2 to get 25(5x-1)(3x+1)
    should i expand all terms then combine and factor?



    2. Relevant equations



    3. The attempt at a solution
    a) i tried using the quotient rule but kept ending up with missing terms...
    from the answer key i know that the answer is (4(x-1))/(x+1)^3
    but i can't get that for the life of me...
     
  2. jcsd
  3. Jan 19, 2012 #2
    Re: Differentiation

    Chain rule on this simplifies it a lot.. (if you know it?)

    [itex]y=u^{2}[/itex]

    [itex]u=\frac{x-1}{x+1}[/itex]


    EDIT: Just in case you don't knnow, take the derivative of y and u then do the following:

    [itex]\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}[/itex]
     
    Last edited: Jan 19, 2012
  4. Jan 19, 2012 #3
    Re: Differentiation

    i do
    however i've never really learned it using substitutions.
    would i bring up the (x+1)^2 to the top, so that the equation becomes (x-1)^2(x+1)^-2?
    or would that further complicate things
     
  5. Jan 19, 2012 #4
    Re: Differentiation

    I editted my post, maybe that will help you
     
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