The differential coefficient of f[log (x)] wi | vedclass

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Question

(C) Given $f(x) = \log x$. We need to find the derivative of $f[\log (x)]$ with respect to $x$. First,substitute $\log x$ into the function $f(x)$: $f

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Given $f(x) = \log x$. We need to find the derivative of $f[\log (x)]$ with respect to $x$. First,substitute $\log x$ into the function $f(x)$: $f[\log (x)] = \log(\log x)$. Now,differentiate $\log(\log x)$ with respect to $x$ using the chain rule: $\frac{d}{dx} [\log(\log x)] = \frac{1}{\log x} \cdot \frac{d}{dx} (\log x)$. Since $\frac{d}{dx} (\log x) = \frac{1}{x}$,we have: $\frac{d}{dx} [\log(\log x)] = \frac{1}{\log x} \cdot \frac{1}{x} = \frac{1}{x \log x}$. Thus,the correct option is $C$.

The differential coefficient of $f[\log (x)]$ with respect to $x$ when $f(x) = \log x$ is:

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