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y=tan^-1[(3x-x^3)/(1-3x^2)],-1/sqrt3ltxl...

`y=tan^-1[(3x-x^3)/(1-3x^2)],-1/sqrt3ltxlt1/sqrt3`

Text Solution

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`y = tan ^(-1)((3x-x^(3))/(1-3x^(2)))`
Let `x + tantheta`
`rArr theta= tan^(-1) x`
`rArr y = tan^(-1)((3tan theta- tan^(3)theta)/(1-3 tan^(2)theta))`
`= tan^(-1) (tan3theta) = 3theta = 3 tan^(-1)x `
`rArr (dy)/(dx) = 2 (d)/(dx) tan^(-1)x = (3)/(1+x^(2))`
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