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

यदि `y=(sin^(-1)x)/(sqrt(1-x^(2)))` है, तो सिद्�

1.	यदि `y=(sin^(-1)x)/(sqrt(1-x^(2)))` है, तो सिद्ध कीजिए कि `(1-x^(2))(dy)/(dx)=xy+1.`
Answer» `y=(sin^(-1)x)/(sqrt(1-x^(2)))` `rArr" "(dy)/(dx)=(d)/(dx)((sin^(-1)x)/(sqrt(1-x^(2))))` `(sqrt(1-x^(2)).(d)/(dx) sin^(-1)x-sin^(-1)x.(d)/(dx)sqrt(1-x^(2)))/((sqrt(1-x^(2)))^(2))` `(sqrt(1-x^(2)).(1)/(sqrt(1-x^(2)))-sin^(-1)x.(1)/(2sqrt(1-x^(2))).(d)/(dx)(1-x^(2)))/((1-x^(2)))` `rArr" "(1-x^(2))(dy)/(dx)=1-(sin^(-1)x)/(sqrt(1-x^(2))).(1)/(2).(-2x)` `rArr" "(1-x^(2))(dy)/(dx)=1+x.y` यही सिद्ध करना था ।