`d/(dt) tan^-1(t)=1/(1+t^2)`

`y=tan^-1(sqrt((1-x)/(1+x)))`

`y'=(1)/(1+((1-x)/(1+x))) * d/(dx)sqrt((1-x)/(1+x))`

`y'=((1+x)/(1+x+1-x)) * d/(dx) (1-x)^(1/2) (1+x)^(-1/2)`

`y'=((1+x)/2) * ((1-x)^(1/2) d/(dx)(1+x)^(-1/2) +(1+x)^(-1/2) d/(dx) (1-x)^(1/2))`

`y'=((1+x)/2)*((1-x)^(1/2) (-1/2)(1+x)^(-3/2) + (1+x)^(-1/2)(1/2)(1-x)^(-1/2)(-1))`

`y'=((1+x)/2) * ((-(1-x)^(1/2))/(2(1+x)^(3/2)) + (-1)/(2(1+x)^(1/2)(1-x)^(1/2)))`

`y'=((1+x)/2) * ((-(1-x)-(1+x))/(2(1+x)(1+x)^(1/2)(1-x)^(1/2)))`

`y'=((1+x)/2) *((-1)/((1+x)(1+x)^(1/2)(1-x)^(1/2)))`

`y'=(-1)/(2(1+x)^(1/2)(1-x)^(1/2))`

`y'=(-1)/(2sqrt(1-x^2))`

## Unlock

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

`d/(dt) tan^-1(t)=1/(1+t^2)`

`y=tan^-1(sqrt((1-x)/(1+x)))`

`y'=(1)/(1+((1-x)/(1+x))) * d/(dx)sqrt((1-x)/(1+x))`

`y'=((1+x)/(1+x+1-x)) * d/(dx) (1-x)^(1/2) (1+x)^(-1/2)`

`y'=((1+x)/2) * ((1-x)^(1/2) d/(dx)(1+x)^(-1/2) +(1+x)^(-1/2) d/(dx) (1-x)^(1/2))`

`y'=((1+x)/2)*((1-x)^(1/2) (-1/2)(1+x)^(-3/2) + (1+x)^(-1/2)(1/2)(1-x)^(-1/2)(-1))`

`y'=((1+x)/2) * ((-(1-x)^(1/2))/(2(1+x)^(3/2)) + (-1)/(2(1+x)^(1/2)(1-x)^(1/2)))`

`y'=((1+x)/2) * ((-(1-x)-(1+x))/(2(1+x)(1+x)^(1/2)(1-x)^(1/2)))`

`y'=((1+x)/2) *((-1)/((1+x)(1+x)^(1/2)(1-x)^(1/2)))`

`y'=(-1)/(2(1+x)^(1/2)(1-x)^(1/2))`

`y'=(-1)/(2sqrt(1-x^2))`