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

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

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`x=tan theta`

we know, ` tan 2 theta=frac{2 tan theta}{1-tan ^{2} theta}=frac{2 x}{1-x^{2}}`

`sin 2 theta=frac{2 tan theta}{1+tan ^{2} theta}=frac{2 x}{1+x^{2}}`

Let `U=sin ^{-1}[frac{2 x}{1+x^{2}}], V=tan ^{-1}(frac{2 x}{1+x^{2}}]`

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