**Who are the experts?**Our certified Educators are real professors, teachers, and scholars who use their academic expertise to tackle your toughest questions. Educators go through a rigorous application process, and every answer they submit is reviewed by our in-house editorial team.

You are watching: Find the derivative of the function. y = arctan 1 − x 1 + x

`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 Now

Start your **48-hour free trial** to unlock this answer and thousands more. Enjoy bromheads.tv ad-free and cancel anytime.

Start your 48-Hour Free Trial

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))`

Approved by bromheads.tv Editorial Team

### Ask a Question

Ask a QuestionSubmit Question

### Popular Questions

See all

## Related Questions

Browse AllMath

Latest answer posted September 10, 2015 at 8:37:48 PM

`y = sin^-1 (2x + 1)` Find the derivative of the function. Simplify where possible.

1 Educator answer

Math

Latest answer posted September 11, 2015 at 12:20:34 AM

`y = cos^-1(sin^-1(t))` Find the derivative of the function. Simplify where possible.

1 Educator answer

Math

Latest answer posted September 05, 2015 at 12:00:40 PM

`y = sqrt(x + sqrt(x + sqrt(x)))` Find the derivative of the function.

4 Educator answers

Math

Latest answer posted October 29, 2012 at 10:03:08 AM

Find the derivative of the function. Simplify if possible.`y = tan^(-1) x^2`

1 Educator answer

Math

Latest answer posted September 23, 2015 at 8:53:51 PM

`y = sqrt((x-1)/(x^4 + 1))` Use logarithmic differentiation to find the derivative of the function.

1 Educator answer

bromheads.tv will help you with any book or any question. Our summaries and analyses are written by experts, and your questions are answered by real teachers. Join bromheads.tv

Apply to be an Educator

See more: Infant Camouflage Car Seat, Camo Infant/Baby Car Seat Cover

### Recommended

### More

©2021 bromheads.tv, Inc. All Rights Reserved