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

If `y=tan^(-1)((3x-x^3)/(1-3x^2)),-1/(sqrt(3))ltxlt1 /(sqrt(3)),` then find `(dy)/(dx)`

Text Solution

Verified by Experts

The correct Answer is:
`(3)/(1+x^(2))`
`y=tan^(-1)((3x-x^(3))/(1-3x^(2)))`
`Put x tan theta.` Then,
`y=tan^(-1)((3 tan theta - tan^(3)theta)/(1-3 tan^(2)theta))`
`=tan^(-1)(tan 3theta)`
`=3theta`
`=3tan^(-1)x`
`therefore" "(dy)/(dx)=(3)/(1+x^(2))`
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