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y=sqrt(x+sqrt(x+sqrt(x+....+oo))). Find ...

`y=sqrt(x+sqrt(x+sqrt(x+....+oo)))`. Find `dy/dx`

Text Solution

Verified by Experts

Given equation can be written as,
`y = sqrt(x+y)`
`y^2 = x+y`
Differentiating both sides w.r.t. x,
`2ydy/dx = 1+ dy/dx`
`dy/dx(2y-1) = 1`
`dy/dx = 1/(2y-1)`, where `y^2 = x+y` and `y gt 0`.
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