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y=tan^(-1)""(3x-x^(3))/(1-3(x^2)),-(1)/(...

`y=tan^(-1)""(3x-x^(3))/(1-3(x^2)),-(1)/(sqrt(3))ltxlt(1)/(sqrt(3))`

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`y=tan^(-1)((3x-x^3)/(1-3x^2))`

Putting `x=tantheta`

`y=tan^(-1)((3tantheta-tan^3theta)/(1-3tan^2theta))`

`y=tan^(-1)(tan3theta)`

`y=3theta`

Putting value of `theta=tan^(-1)x`

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

Differentiating both sides w.r.t. x

`dy/dx=(d(3(tan^-1x)))/dx`

`dy/dx=3(d(tan^-1x))/dx`

`dy/dx=3(1/(1+x^2))`

`dy/dx=3/(1+x^2)`
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