यदि `y = (sin ^(-1) x)/(sqrt(1-x^(2)))` तो सिद्ध कीजिए कि ` (1-x)^(2) (dy)/(dx) = xy +1`

Explanation

` y = ( sin^(-1)x )/sqrt( 1 - x^(2))`
दोनों पक्षों का x के साक्षेप अवकलन करने पर
` dy/dx = ( (sqrt(1-x^(2))) ( 1/(sqrt(1-x^(2)))) -sin ^(-1) x { 1/(2sqrt(1-x^(2)))(-2x)})/(sqrt(1-x^(2)))`
या ` dy/dx = ((( x sin^(-1) )/((sqrt(1-x^(2))))))/ ((1- x^(2) )) `
या ` (1-x^(2)) dy/dx = 1 + xy " " [ :' (sin^(-1)x)/(sqrt(1-x^(2)))= y ] `
या ` ( 1- x^(2)) dy/dx = xy + 1 `