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y=sin^(-1)[sqrt(x-a x)-sqrt(a-a x)] then...

`y=sin^(-1)[sqrt(x-a x)-sqrt(a-a x)]` then find `dy/dx`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2sqrt(x(1-x)))`
`y=sin^(-1)[sqrt(x-ax)-sqrt(a-ax)]`
`=sin^(-1)[sqrt(x)sqrt(1-a)-sqrt(a)sqrt(1-x)]`
`=sin^(-1)[sqrt(x)sqrt(1-(sqrt(a))^(2))-sqrt(a)sqrt(1-(sqrt(x))^(2))]`
`=sin^(-1)sqrt(x)-sin^(-1)sqrt(a)`
`therefore" "(dy)/(dx)=(1)/(sqrt(1-x))xx(1)/(2sqrt(x))`
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