- #1

smith007

- 10

- 0

## Homework Statement

Find the derivative of the function. Simplify where possible.

arctan(x - sqrt(1+x

^{2}))

## Homework Equations

Chain rule

## 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.