Question

Find `bb(dy/dx)` in the following:

`y = sin^(-1)((2x)/(1+x^2))`

Answer 1

y = `sin^-1 ((2x)/(1 + x^2))`

Let, x = tan θ

⇒ θ = tan⁻¹ x

∴ `y = sin^-1 ((2  tan theta)/(1 + tan^2 theta))`

= `sin^-1 (sin 2 theta)  ... [because sin 2 theta = (2 tan theta)/(1 + tan^2 theta)]`

= 2 θ 

y = 2 tan⁻¹ x

∴ `dy/dx = 2 d/dx tan^-1 x`

`dy/dx = 2/(1 + x^2)`