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If (x+sqrt(1+x^(2))) (y+sqrt(1+y^(2))) =...

If `(x+sqrt(1+x^(2))) (y+sqrt(1+y^(2))) =1` then `(dy)/(dx)` may be equals to

A

0

B

`-1`

C

1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`x+sqrt(1+x^(2)) = (1)/(sqrt(1+y^(2))+y) = sqrt(1+y^(2))-y` ....(1)
`y+sqrt(1+y^(2)) = (1)/(sqrt(1+x^(2))+x) = sqrt(1+x^(2))-x` ....(2)
Adding (1) and (2) we get
`x + y = 0 rArr y - x`
`(dy)/(dx) = -1`
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