Question

if `y= (sin ^(-1)x)/(sqrt(1-x^2))` then prove that `(1-x)^2) .d/dx=xy+1`

Answer 1

`y=(sin^1x)/(sqrt(1-x^(2)))`
`rArr dy/dx=d/dx((sin^(-1)x)/(sqrt(1-x^(2))))`
`sqrt(1-x^(2))d/dxsin ^(-1)x-sin^(-1)x`
`=(" ".d/dxsqrt(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))d/dx=1 +x.y`
Hence Proverd