यदि ` y = cos^(-1) ( 2x sqrt(1 - x^(2))),` तो सिद्ध कीजिए कि `(dy)/(dx) = 2 ( 1/sqrt(1-x^(2)))`

Explanation

` :' y = cos^(-1) ( 2x sqrt( 1 - x^(2))) `
माना ` x = sin theta ,` तब
` :. y = cos^(-1) ( 2 sin theta sqrt( 1 - sin ^(2) theta ))`
` = cos ^(-1) ( 2 sin theta cos theta ) `
` = cos^(-1) ( sin 2 theta ) `
` = cos ^(-1) [ cos ( 90^(@) - 2 theta )] `
` y = 90^(@) - 2 theta `
या ` y = 90^(@) - 2 sin^(-1) x `
` dy / dx = 0-2 ( 1/sqrt( 1-x^(2)))`
` dy/dx = -2 ( 1/(sqrt(1-x^(2))))`