Question

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

Answer 1

`-(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)`