यदि ` y= sin ^(-1) [x sqrt (1-x) -sqrt ( x)sqrt(1-x^(2) )]` तब `(dy)/(dx) ` का मान ज्ञात कीजिए|

Explanation

`y=sin ^(-1) [x sqrt (1-x) -sqrt(x) sqrt(1-x^(2))]`
माना ` x= sin theta, sqrt x =sin phi, ` तब
` y= sin ^(-1) [sin theta cos phi - sin phi cos theta ] =sin ^(-1) [sin (theta -phi )] `
` y= theta-phi rArr " "sin ^(-1) x- sin ^(-1) sqrt (x) `
` therefore (dy)/(dx) =(d)/(dx) { sin ^(-1) x-sin ^(-1) sqrtx) `
` " "= (d)/(dx) (sin ^(-1) x) -(d)/(dx) (sin ^(-1) sqrt(x))`
` " "= [ (1)/(sqrt( 1-x^(2)) )-(1)/(2sqrt(x)*sqrt(1-x))]`