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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,\ 1)`

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Verified by Experts

Given that,
`y=tan^(-1)((2x)/(1-x^2))`,`x in (-1,\ 1)`
`x=tan theta`
`y=tan^-1 [(2tan theta)/(1-tan^2 theta)]`
`y=tan^-1 (tan2theta)`
`x in (-1,\ 1)`
`=>theta in (-pi/4,pi/4)`
`=>2theta in (-pi/2,pi/2)`
`y=2theta`
`=>y=2tan^-1 x`
`(dy)/(dx)=2*d/(dx) tan^-1 x`
`=2/(1+x^2)`
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