1.

`(dy)/(dx)` ज्ञात कीजिए : `y=sin^(-1)((1-x^(2))/(1+x^(2))),0 lt x lt 1`

Answer» `y=sin^(-1)((1-x^(2))/(1+x^(2)))" "{:("माना "x=tan theta),(rArr theta= tan^(-1)x):}`
`rArr" "y=sin^(-1)((1-tan^(2) theta)/(1+tan^(2) theta))`
`=sin^(-1)((cos^(2) theta-sin^(2)theta)/(cos^(2)theta+sin^(2) theta))`
`=sin^(-1)(cos 2 theta)=sin^(-1)sin((pi)/(2)-2 theta)`
`=(pi)/(2)-2 theta=(pi)/(2)-2 tan^(-1)x`
`rArr" "(dy)/(dx)=(d)/(dx)((pi)/(2)-2 tan^(-1)x)`
`=0-(2xx1)/(1+x^(2))=-(2)/(1+x^(2))`


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