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Homework Help: Derivative. arctan(x - sqrt(1+x^2))

  1. Oct 9, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the derivative of the function. Simplify where possible.
    arctan(x - sqrt(1+x2))

    2. Relevant equations

    Chain rule

    3. The attempt at a solution

    let u = x - sqrt(1+x2)

    y = tan-1(u)

    dy/du = 1/(1+ u2)
    sub in u.
    dy/du = 1/1 + (x - sqrt(1+x2))2


    du/dx = 1 - 1/2 (1+x2)-1/2 (2x)

    dy/dx = (1/1 + (x - sqrt(1+x2))2) (1 - 1/2 (1+x2)-1/2 (2x))


    I always seem to forget 1 term and I am basically wondering if my method here is correct.
     
  2. jcsd
  3. Oct 9, 2008 #2

    Redbelly98

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    Looks right to me. It would be good to include another pair of parentheses in the first term:

    dy/dx = (1/(1 + (x - sqrt(1+x2))2)) (1 - 1/2 (1+x2)-1/2 (2x))
     
  4. Oct 9, 2008 #3
    Thank you.

    I am new to the forums here and I must say they are great!
     
  5. Oct 9, 2008 #4

    Redbelly98

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    You're welcome, and welcome to PF.
     
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