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If x=sqrt(1-y^2), then (dy)/(dx)=...

If `x=sqrt(1-y^2)`, then `(dy)/(dx)=`

A

0

B

x

C

`(sqrt(1-y^2))/(1-2y^2)`

D

`(sqrt(1-y^2))/(1+2y^2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`x=ysqrt(1-y^(2))`
Differentiate with respect to x.
`1=(dy)/(dx)sqrt(1-y^(2))+y.(1)/((2sqrt(1-y^(2))).(-2y).(dy)/(dx)`
`implies1=(dy)/(dx)sqrt(1-y^(2))-(y^(2))/(sqrt(1-y^(2)).(dy)/(dx)`
`implies1=(dy)/(dx)[(1-y^(2)-y^(2))/(sqrt(1-y^(2)))]implies1=(dy)/(dx)[(1-2y^(2))/(sqrt(1-y^(2)))]`
`(dy)/(dx)=(sqrt(1-y^(2)))/(1-2^(2))`
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