If `y=sin^(-1)((2x)/(1+x^2))` , write the value of `(dy)/(dx)` for `x >1` .

Explanation

We have, `{y}=sin ^{-1}(frac{2 x}{1+x^{2}})`

Putting `x=tan theta`


`Rightarrow 1 < tan theta < oo `

`Rightarrow frac{pi}{4} < theta < frac{pi}{2} `

`Rightarrow frac{pi}{2} < 2 theta < pi`

`therefore y=sin ^{-1}(sin 2 theta)`

`Rightarrow y=sin ^{-1}{sin (pi-2 theta)} `

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