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Question
Find `("d"y)/("d"x)`, if y = `tan^-1 ((3x - x^3)/(1 - 3x^2)), -1/sqrt(3) < x < 1/sqrt(3)`
Solution
Put x = tan θ
Where `(-pi)/6 < θ < pi/6`
Therefore, y = `tan^-1 ((3tan theta - tan^3theta)/(1 - 3 tan^2theta))`
= `tan^-1 (tan 3theta)`
= 3θ ...`(because (-pi)/2 < 3theta < pi/2)`
= 3tan–1x
Hence, `("d"y)/("d"x) = 3/(1 + x^2)`
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