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"If "xsqrt(1+y)+ysqrt(1+x)=0," prove tha...

`"If "xsqrt(1+y)+ysqrt(1+x)=0," prove that "(dy)/(dx)=-(1)/((x+1)^(2)).`

A

`1+x`

B

`(1+x)^-2`

C

`-(1+x)^-1`

D

`-(1+x)^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`xsqrt(1+y)+ysqrt(1+x)=0impliesx^(2)(1+y)=y^(2)(1+x)`
`implies(x-y)(x+y+xy)=0impliesx+y+xy=0` `[xney]`
`implies(dy)/(dx)=(-1)/((1+x)^(2))`
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