Differentiate `tan^(-1)((3x-x^3)/(1-3x^2)),if` `-1/sqrt(3)ltxlt1 /sqrt(3)`(2)`xgt1/sqrt(3)``( 3).`x lt-1/sqrt(3)`

Explanation

`f(x) = tan^-1 [ (3x-x^3)/(1-3x^2)]`

let `x= tan theta`

`theta= tan^-1 x`

so `f(x) = tan^-1 [ tan 3 theta] `

`f(x) = 3 theta`

`f(x) = 3 tan^-1 x`

`f'(x) = 3/(1 + x^2) `

ii) `x > 1/sqrt3`

...