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

If `y=tan^-1((3x-x^2)/(1-3x^2)), (-1)/sqrt3ltxlt1/sqrt3 `
Find `(dy)/(dx)`

Text Solution

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`y=tan^-1((3x-x^3)/(1+3x^2))=3tan^-1xtherefore(dy)/(dx)=3xx1/(1+x^2)=3/(1+x^2)tan^-1((3x-x^2)/(1+3x^2))=3tan^-1x`
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