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Derivative: arctan(sqrt((1-x)/(1+x)))

  1. Jan 18, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the derivative:
    arctan[tex]\sqrt{(1-x)/(1+x)}[/tex]


    2. Relevant equations
    Chain Rule, Quotient Rule


    3. The attempt at a solution
    I've gotten to a point where I feel like I either don't know how to simplify from this point, or I've done something wrong:
    [1/(1+((1-x)/(1+x)))] * [(-[tex]\sqrt{(1+x)}[/tex]/2*[tex]\sqrt{1-x}[/tex])-([tex]\sqrt{1-x}[/tex]/2*[tex]\sqrt{1+x}[/tex])]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 18, 2009 #2

    Mark44

    Staff: Mentor

    It looks about right (I didn't check that closely), but I don't understand some of what you have shown, namely the parts where it looks like you're dividing by 2.

    Your derivative should look like this:
    1/(1 + (sqrt(quotient in radical))^2) * 1/2(quotient in radical)^(-1/2) * (derivative of quotient inside radical)

    The first factor you show looks fine, but I don't understand what you have after that.
     
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