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If y=sqrt(x+sqrt(x+sqrtx+............oo...

If `y=sqrt(x+sqrt(x+sqrtx+............oo))`, then `(dy)/(dx)`

A

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

B

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

C

`(1)/(sqrt(1+4x))`

D

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

Text Solution

Verified by Experts

`y^(2)=x+y or (dy)/(dx)=(1)/(2y-1)`
`"Also, "y=(x)/(y)+1or (dy)/(dx)=(y)/(2x+y)`
`"Also, "y^(2)-y-x=0`
`"or "y=(1+sqrt(1+4x))/(2)" "("as " y gt0)`
`"or "y'=(1)/(4)(4)/(sqrt(1+4x))=(1)/(sqrt(1+4x))`
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