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

Differentiate `sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2))` , with respect to `x` , if `x in (0,\ 1)`.

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Given that,
`y=sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2))`
`x in (0,\ 1)`.
`y=tan theta`
`y= sin^-1 [(2tantheta)/(1+tan^2 theta)]+cos^-1 [(1-tan^2theta)/(1+tan^2theta)]`
`=>y=sin^-1 (sin2theta)+cos^-1(cos2theta)`
`x in (0,\ 1)`
`=>tan theta in (0,\ 1)`
`=>theta in (0,pi/4)`
`=>2theta in (0.pi/2)`
`y=2theta+2theta`
`=>y=4theta`
`=>y=4 tan^-1 x`
`(dy)/(dx)=4/(1+x^2)`
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