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Differentiate tan^(-1)((2x)/(1-x^2)) wit...

Differentiate `tan^(-1)((2x)/(1-x^2))` with respect to `x` , if `x in (1,\ oo)`

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Verified by Experts

Given that,
`y=tan^(-1)((2x)/(1-x^2))`, `x in (1,\ oo)`
`x=tan theta`
`y=tan^-1 [(2tan theta)/(1-tan^2 theta)]`
`y=tan^-1 (tan2theta)`
`x in (1,\ oo)`
`=>theta in (pi/4,-pi/2)`
`=>2theta in (pi/2,pi)`
`y=2theta-pi`
`=>y=2tan^-1 x-pi`
`(dy)/(dx)=2*d/(dx) tan^-1 x`
`=2/(1+x^2)`
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
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  2. Differentiate tan^(-1)((2x)/(1-x^2)) with respect to x , if x in (-oo,...

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  8. Differentiate sin^(-1)((2x)/(1+x^2)) with respect to x , when x in (1,...

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  14. Differentiate cos^(-1)((2x)/(1+x^2)) , -1ltxlt1 with respect tox

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