यदि ` y = sin^(-1) x` है तो दर्शाइए कि ` (1-x)^(2) (d^(2)y)/(dx^(2)) - x (dy)/(dx) = 0 ` है ।

Explanation

` :' y = sin^(-1) x `
` :. (dy)/(dx) = 1/(sqrt( 1-x^(2)))`
पुनः अवकलन करने पर ,
` (d^(2)y)/(dx^(2)) = ((1-x^(2))^(1/2)* d/(dx) (1) -1 d/(dx) (1-x^(2))^(1/2))/(1-x^(2))`
या `(1-x)^(2) (d^(2)y)/(dx^(2)) = ( 1-x^(2))^(1/2)0-1 xx 1/2 (1-x^(2)) ^(1/2) xx (-2x)`
या ` ( 1- x)^(2) (d^(2)y)/(dx^(2)) = x/(sqrt(1- x^(2)))`
या ` ( 1-x^(2)) (d^(2)y)/(dx^(2)) = x/(sqrt(1-x^(2)))`
या ` ( 1-x^(2) ) (d^(2)y)/(dx^(2)) = x xx (dy)/(dx) `
या ` ( 1 - x^(2)) (d^(2)y)/(dx^(2)) - x (dy)/(dx) = 0 `