Question

please tell me fast ..​

Answer 1

Let tan⁻¹ x = y

x = tan y

sin⁻¹(2x/(1 + x²)) = sin⁻¹(2tan y / (1 + tan² y))

                           = sin⁻¹(sin 2y) [ sin 2y = 2tan y/(1 + tan²y) ]

                           = 2y

the question is differentiation of sin⁻¹(2x/(1+x²)) w.r.t tan⁻¹ x

Here,

sin⁻¹(2x/(1 + x²)) = 2y

tan⁻¹ x = y

So, differentiaiton of 2y w.r.t y

d/dy (2y) = 2.

The answer is 2.