Differentiate `tan^(-1)((3x-x^3)/(1-3x^2))` , if `-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`

...