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Find dy/dx If y=sin^(-1)(frac(1-x^2)(1+x...

Find `dy/dx` If `y=sin^(-1)(frac(1-x^2)(1+x^2))` , `0 < x < 1`

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`y=sin^-1((1-x^2)/(1+x^2))=pi/2-cos^-1((1-x^2)/(1+x^2))=pi/2-2tan^-1xtherefore(dy)/(dx)=0-2xx1/(1+x^2)=2/(1+x^2)sin^-1x=pi/2cos^-1x`
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