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Homework Help: Arithmetic Question for Finding Derivative using Quotient Rule

  1. Jul 3, 2011 #1
    1. The problem statement, all variables and given/known data

    Find dy/dx for the following function:

    y = (11-cos(x))/(2+cos(x))

    2. Relevant equations

    Quotient Rule:

    y'= ((g(x))(f'(x)) - (f(x))(g'(x)))/ (g(x)^2)

    3. The attempt at a solution

    I used the quotient rule to come up with this:

    y'= ((2+cos(x))(sin(x)) - (11-cos(x))(-sin(x))) / ((2+cos(x))^2)

    Now, the trouble that I am having is simplifying this.

    The final answer should turn out to be :


    I am overlooking some basic arithmetic here, but I can't seem to find out what I am missing. Am I supposed to multiply out the expressions first and then combine like terms? Basically, how do I go from the expanded version to the simplified version? Thank you
  2. jcsd
  3. Jul 3, 2011 #2


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    Gold Member

    Yes try expanding it; simplifying it to the required expression is just a matter of collecting like terms
  4. Jul 3, 2011 #3


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    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Your denominator looks to be in the same form as the desired answer.

    Play around with the numerator.
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