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If y=sqrt(x+sqrt(x+sqrt(x+\ dotto\ oo)))...

If `y=sqrt(x+sqrt(x+sqrt(x+\ dotto\ oo)))` , prove that `(dy)/(dx)=1/(2\ y-1)`

Text Solution

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`y=sqrt(x+sqrt(x+sqrt(+…..oo)))`
`y=sqrt(x+y)`
`rArr y^2x+y`
`rArr 2dy dy/dx =1 + dy/dx`
`rArr (2y -1) dy/dx =1`
` rArr dy/dx =(1)/(2y -1)`
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