Question

If y = `sqrt(log x + sqrt(log x + sqrt(log x + .... ∞)`, then `(dy)/(dx)` = ______.

विकल्प

• `x/(2y - 1)`

• `x/(2y + 1)`

• `1/(x(2y - 1))`

• `1/(x(1 - 2y))`

Answer 1

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)`