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

Explanation

यहाँ ` y= sin ^(-1) (x sqrt(1-x )- sqrt(x) sqrt(1-x^(2)))`
` " "= sin ^(-1) {x sqrt(1-(sqrt(x))^(2))- sqrt(x) sqrt(1-x^(2))}`
` " "= sin ^(-1)x -sin ^(-1) sqrt(x)`
` (because sin ^(-1) a -sin ^(-1) b sin ^(-1) (asqrt (1-b^(2))-bsqrt(1-a^(2)))`
` rArr " "(dy)/(dx) = (1)/(sqrt(1-x ^(2) ))- (1) /(sqrt(1-(sqrt(x))^(2)))*(d)/(dx) (sqrt(x))`
` " "= (1)/(sqrt(1-x^(2)))-(1)/(sqrt(1-x ))*(1)/(2sqrt(x))`
` = (1)/(sqrt(1-x^2))-(1)/(2)(1)/(sqrt(x-x^(2)))`