(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the derivative of the function. Simplify where possible.

arctan(x - sqrt(1+x^{2}))

2. Relevant equations

Chain rule

3. The attempt at a solution

let u = x - sqrt(1+x^{2})

y = tan^{-1}(u)

dy/du = 1/(1+ u^{2})

sub in u.

dy/du = 1/1 + (x - sqrt(1+x^{2}))^{2}

du/dx = 1 - 1/2 (1+x^{2})^{-1/2}(2x)

dy/dx = (1/1 + (x - sqrt(1+x^{2}))^{2}) (1 - 1/2 (1+x^{2})^{-1/2}(2x))

I always seem to forget 1 term and I am basically wondering if my method here is correct.

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

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