Differentiate `sin^(-1){sqrt(1-x^2)},\ 0

Explanation

Solution:

`u=\sin ^{-1}{\sqrt{1-x^{2}}\}`

`0
`u=\sin ^{-1}\{\sqrt{1-\cos ^{2} \theta}\}=\sin ^{-1}\{\frac{1}{\sin ^{2} \theta}\}`

=`\sin ^{-1}(\sin \theta)=0 .`

`\theta=\cos ^{-1} x`

`u=\cos ^{-1} x`

`[du]/[dx]=-1/sqrt(1-x^2)`