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x y=(x+y)6na n d(dy)/(dx)=y/x t h e nn= ...

`x y=(x+y)6na n d(dy)/(dx)=y/x t h e nn=` `1` b.`2` c. `3` d. `4`

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Taking log on both sides we get
`nlog(x+y)=logx+logy`
Differentiating w.r.t. x, we get
`(n)/(x+y)[1+(dy)/(dx)]=(1)/(x)+(1)/(y)(dy)/(dx)`
`rArr" "(dy)/(dx)=(y)/(x)[(x+y-nx)/(ny-x-y)]`
`rArr" "n=2" for "(dy)/(dx)=(y)/(x)`
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