What's the derivative of $arctan sqrt [ (1-x)/(1+x)]$ ?

Question

What's the derivative of $arctan sqrt [ (1-x)/(1+x)]$ ?

1 Answer

Impact of this question

1806 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-07T12:15:37

$-(1/2)(1/sqrt(1-x^2))$

Explanation:

Substitute x = cos t and use formulas
cos t = $(2 cos^2( t/2) - 1) = (1-2 sin^2( t/2))$ .
the given function y = arc tan (tan $t/2$ ) = $t/2$ .
Reverting to x, y = $(1/2) cos^(-1)x$ .
$dy/dx=-(1/2)(1/sqrt(1-x^2)$

Science

Math

Humanities

... and beyond

What's the derivative of $arctan sqrt [ (1-x)/(1+x)]$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What's the derivative of arctan sqrt [ (1-x)/(1+x)]arctan sqrt [ (1-x)/(1+x)]?

1 Answer

Explanation:

Related questions

Impact of this question

What's the derivative of $arctan sqrt [ (1-x)/(1+x)]$ ?