Differentiate the following w.r.t. x : sin [2 tan^-1 (√(1 - x)/(1 + x))]

Question

Differentiate the following w.r.t. x :

\(sin \left[2\,tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\right]\)

sin [2 tan^-1 (√(1 - x)/(1 + x))]

Answer 1

Let y = sin [2 tan^-1 (√(1 - x)/(1 + x))]

Put x = cos θ, Then θ = cos^-1 x and