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Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/...

Let `y=sqrt(x+sqrt(x+sqrt(x+oo)))` , `(dy)/(dx)` is equal to

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

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

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

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

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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