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Differentiate sin^(-1)((2x)/(1+x^2)) wit...

Differentiate `sin^(-1)((2x)/(1+x^2))` with respect to `x` , when `x in (1,\ oo)`

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