frac{d}{dx} log(log x) = | vedclass

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Question

(C) To find the derivative of $\log(\log x)$ with respect to $x$,we use the chain rule.Let $u = \log x$. Then the expression becomes $\frac{d}{dx} \lo

Vedclass · Accepted Answer

$(x \log x)^{-1}$

Vedclass · Answer

(C) To find the derivative of $\log(\log x)$ with respect to $x$,we use the chain rule.Let $u = \log x$. Then the expression becomes $\frac{d}{dx} \log(u)$.By the chain rule,$\frac{d}{dx} \log(u) = \frac{d}{du} \log(u) \cdot \frac{du}{dx}$.We know that $\frac{d}{du} \log(u) = \frac{1}{u}$ and $\frac{du}{dx} = \frac{d}{dx} \log x = \frac{1}{x}$.Substituting these values back,we get $\frac{1}{\log x} \cdot \frac{1}{x} = \frac{1}{x \log x}$.This can be written as $(x \log x)^{-1}$.Therefore,the correct option is $C$.

$\frac{d}{dx} \log(\log x) = $

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