Differentiate the following with respect to x | vedclass

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(A) Let $y = \log (\log x)$.By using the chain rule,we differentiate with respect to $x$:$\frac{dy}{dx} = \frac{d}{dx} [\log (\log x)]$Applying the ch

Vedclass · Accepted Answer

$\frac{1}{x \log x}$

Vedclass · Answer

(A) Let $y = \log (\log x)$.By using the chain rule,we differentiate with respect to $x$:$\frac{dy}{dx} = \frac{d}{dx} [\log (\log x)]$Applying the chain rule,where the derivative of $\log(u)$ is $\frac{1}{u} \cdot \frac{du}{dx}$:$\frac{dy}{dx} = \frac{1}{\log x} \cdot \frac{d}{dx} (\log x)$Since the derivative of $\log x$ is $\frac{1}{x}$:$\frac{dy}{dx} = \frac{1}{\log x} \cdot \frac{1}{x}$Thus,the final result is:$\frac{dy}{dx} = \frac{1}{x \log x}$,for $x > 1$.

Differentiate the following with respect to $x$: $\log (\log x)$,where $x > 1$.

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