If y = x + x + x + ..... , then dy dx = - Vidyadip

MCQ

If $y = \sqrt {\log x + \sqrt {\log x + \sqrt {\log x + .....\infty } } } $, then ${{dy} \over {dx}} = $

A
${x \over {2y - 1}}$
B
${x \over {2y + 1}}$
✓
${1 \over {x(2y - 1)}}$
D
${1 \over {x(1 - 2y)}}$

✓

Answer

Correct option: C.

${1 \over {x(2y - 1)}}$

c
(c) $y = \sqrt {\log x + y} \Rightarrow {y^2} = \log x + y$

$ \Rightarrow 2y\frac{{dy}}{{dx}} = \frac{1}{x} + \frac{{dy}}{{dx}} $

$\Rightarrow \frac{{dy}}{{dx}} = \frac{1}{{x(2y - 1)}}$.

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