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" If "y=sqrt(logx+sqrt(logx+sqrt(logx+.....

`" If "y=sqrt(logx+sqrt(logx+sqrt(logx+...oo)))," then "(dy)/(dx)` is

A

`(x)/(2y-1)`

B

`(x)/(2y+1)`

C

`(1)/(x(2y-1)`

D

`(1)/(x(1-2y)`

Text Solution

Verified by Experts

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