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  4. If y √log x+√log x +√log x + ...∞, then (dy/dx) is

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Q. If $y \sqrt{log\,x+\sqrt{log\,x +\sqrt{log\,x + ...\infty}}}$, then $\frac{dy}{dx}$ is

Limits and Derivatives

Solution:

$y = \sqrt{log\,x + y}$
or $y^2 = log\,x + y$
or $2y \frac{dy}{dx} = \frac{1}{x} + \frac{dy}{dx} $ or $\frac{dy}{dx} = \frac{1}{x(2y -1)}$