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Question
Find `dy/dx` in the following:
`y = tan^(-1) ((3x -x^3)/(1 - 3x^2)), - 1/sqrt3 < x < 1/sqrt3`
Solution
Here y = `tan^-1 ((3x - x^3)/(1 - 3x^2))`
Putting x = `tan theta`,
`therefore y = tan^-1 ((3 tan theta - tan^3 theta)/(1 - 3 tan^2 theta)) = tan^-1 tan 3 theta`
`y = 3 theta = 3 tan^-1 x, ... [because theta = tan^-1 x]`
On differentiating with respect to x,
`dy/dx = 3 d/dx tan^-1 x`
`= 3/(1 + x^2)`
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