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Question
`"If" y = sqrt(logx + sqrt(log x + sqrt(log x + ... ∞))), "then show that" dy/dx = (1)/(x(2y - 1).`
Solution
`y = sqrt(logx + sqrt(log x + sqrt(log x + ... ∞)))`
∴ `y^2 = log x + sqrt(log x + sqrt(log x + ... ∞)`
∴ y2 = log x + y
Differentiating both sides w.r.t. x, we get,
`2y. dy/dx = (1)/x + dy/dx`
∴ `(2y - 1) dy/dx = (1)/x`
∴ `dy/dx = (1)/(x(2y - 1)`.
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