Differentiate `sin^(-1)((2x)/(1+x^2))` with respect to `tan^(-1)x ,-1ltxlt1` .

Explanation

Let `u=sin^(-1)((2x)/(1+x^2))`
taking `x=tan theta`
`=>u=sin^(-1)((2 tan theta)/(1+tan^2 theta))`
`=>u=sin^(-1) sin 2 theta`
`=>u=2 theta`
`=>u=2tan^-1x`
`=>(du)/(dx)= 2/(1+x^2)`
again `v=tan^-1 x`
`=>(dv)/(dx)=1/(1+x^2)`
`=>(du)/(dv)=2`