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Question
If y = `sqrt(log x + sqrt(log x + sqrt(log x + .... ∞)`, then `(dy)/(dx)` = ______.
Options
`x/(2y - 1)`
`x/(2y + 1)`
`1/(x(2y - 1))`
`1/(x(1 - 2y))`
MCQ
Fill in the Blanks
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Solution
If y = `sqrt(log x + sqrt(log x + sqrt(log x + .... ∞)`, then `(dy)/(dx)` = `underlinebb(1/(x(2y - 1)))`.
Explanation:
y = `sqrt(log x + y)`
`\implies` y2 = log x + y
`\implies` `2y (dy)/(dx) = 1/x + (dy)/(dx)`
`\implies (dy)/(dx) = 1/(x(2y - 1)`
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Derivative of Implicit Functions
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