Let y = log(log(X)) Then Find The Value Of ey dy/dx.

Sol:

Given:

y = log(log(x))

By differentiating both the sides with respect to x we get,

\(\frac{dy}{dx} = \frac{1}{log x} \; \frac{d}{dx} (log x)\) \(\Rightarrow \frac{dy}{dx} = \frac{1}{log x} * \frac{1}{x}\) \(\Rightarrow log x * \frac{dy}{dx} = \frac{1}{x} \) \((since e^{y} = e^{log(log x)} = log x)\) \(\Rightarrow e^{y}\frac{dy}{dx} = \frac{1}{x}\)

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