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If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((...

If `y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx)` is equal to (a)`x+y` (b) `1+x y` (c) `1-x y` (d) `x y-2`

A

x+y

B

1+xy

C

1-xy

D

xy-2

Text Solution

Verified by Experts

`y=(sin^(-1))/(sqrt(1-x^(2)))`
`therefore" "(dy)/(dx)=(sqrt(1-x^(2))(1)/(sqrt(1-x^(2)))-(sin^(-1)x)(1)/(2)((-2x))/(sqrt(1-x^(2))))/(1-x^(2))`
`"or "(1-x^(2))(dy)/(dx)=1+x((sin^(-1)x)/(sqrt(1-x^(2))))=1+xy`
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