MCQ
Derivative of $\log _{e^2}(\log x)$ with respect to $x$ is
- A$\frac{2}{x \log x}$
- B$\frac{1}{x \log x}$
- C$\frac{1}{x \log x^2}$
- D$\frac{2}{\log x}$
(c) : Let $y=\log _{e^2}(\log x)=\frac{\log (\log x)}{\log e^2}=\frac{\log (\log x)}{2}$
Now, $\frac{d y}{d x}=\frac{1}{2} \frac{d}{d x}[\log (\log x)]=\frac{1}{2} \times \frac{1}{\log x} \cdot \frac{d}{d x}(\log x)$
$
=\frac{1}{2 \log x} \times \frac{1}{x}=\frac{1}{x \log x^2}
$
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