Question

Find `(dy)/(dx)`, if `y = sin^-1 ((2x)/(1 + x^2))`

Options

• `1 + x^2`

• `1/(1 + x^2)`

• `(1 + x^2)/2`

• `2 + x^2`

Answer 1

`1/(1 + x^2)`

Explanation:

`y = sin^-1 ((2x)/(1 + x^2))`, put `x = tan theta`

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

= `sin^-1 (sin^2 theta)`

= `2theta = 2tan^-1x`

∴ `(dy)/(dx) = 2/(1 + x^2)`