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Differentiate tan^(-1)((3x-x^3)/(1-3x^2)...

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

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Verified by Experts

`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] `
`-1/(sqrt(3))ltxlt1/(sqrt(3))`
`=>-pi/6 lt theta lt pi/6`
`=>-pi/2 lt 3theta lt pi/2`
`f(x)= 3 theta`
`=>f(x)= 3 tan^-1 x`
`=> f'(x) = 3/(1+x^2)`
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