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Find (dy)/(dx) for the function: y=sin^(...

Find `(dy)/(dx)` for the function: `y=sin^(-1)sqrt((1-x))+cos^(-1)sqrt(x)`

Text Solution

Verified by Experts

The correct Answer is:
`(-1)/(sqrt(x-x^(2)))`
`sin^(-1)sqrt(1-x)=sin^(-1)sqrt(1(sqrt(x))^(2))=cos^(-1)sqrt(x)`
`therefore" "y=2 cos^(-1)sqrt(x)`
`"or "(dy)/(dx)=2xx(-1)/(sqrt(1-x))xx(1)/(2sqrt(xx))=(-1)/(sqrt(1-x^(2))`
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