Find `(dy)/(dx),` if `y=sin^(-1)[xsqrt(\ 1-x)-\ sqrt(x)\ sqrt(1-x^2)\ ]\ `

Explanation

Let `x = sintheta`, then `sin^-1x = theta`

Then, our given equation becomes,

`y = theta+sin^-1(sqrt(1-sin^2theta))`

`y = theta+sin^-1(costheta)`

`y = theta+sin^-1(sin(pi/2-theta))`

`y = theta+pi/2 -theta`

`y = pi/2`

`:. dy/dx = 0`