The derivative of y = ^2 [ ⁻¹ ( 1-x 1+x ) ] is

Step-by-step solution

Let = ⁻¹ ( 1-x 1+x ) = 1-x 1+x The given function can be written as y = ^2 . Using the trigonometric identity ^2 = 1 ^2 = 1 1 + ^2 , we get: y = 1 1 + ( 1-x 1+x )^2 y = 1 1 + 1-x 1+x y = 1+x (1+x) + (1-x) y = 1+x 2 Differentiating with respect to x : dy dx = d dx ( 1 2 + x 2 ) = 1 2 Answer: 1 2