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

  • Thread starter smith007
  • Start date
  • #1
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Homework Statement



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

Homework Equations



Chain rule

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.
 

Answers and Replies

  • #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))
 
  • #3
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Thank you.

I am new to the forums here and I must say they are great!
 
  • #4
Redbelly98
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You're welcome, and welcome to PF.
 

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