If y = {2tan^-1 √((1 - x)/(1 + x))}, show that dy/dx = -x/√(1 - x^2).

Question

If y = sin\(\left\{2tan^{-1}\left(\sqrt{\cfrac{1-\text x}{1+\text x}}\right)\right\},\) show that dy/dx = \(\cfrac{-\text x}{\sqrt{1-\text x^2}}.\)

{2tan^-1 √((1 - x)/(1 + x))}, dy/dx= -x/(√1 - x²).

Answer 1

Given: Value of y =  sin\(\left\{2tan^{-1}\left(\sqrt{\cfrac{1-\text x}{1+\text x}}\right)\right\}\) 

To Prove:  dy/dx = \(\cfrac{-\text x}{\sqrt{1-\text x^2}}\)