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Question
If \[y = \log_a x, \text{ find } \frac{dy}{dx} \] ?
Solution
\[\text{ We have, y} = \log_a x\]
\[ \Rightarrow y = \frac{\log x}{\log a} \left[ \because \log_a b = \frac{\log b}{\log a} \right]\]
\[\Rightarrow \frac{dy}{dx} = \frac{1}{\log a}\frac{d}{dx}\left( \log x \right)\]
\[ \Rightarrow \frac{dy}{dx} = \frac{1}{\log a}\left( \frac{1}{x} \right)\]
\[ \Rightarrow \frac{dy}{dx} = \frac{1}{x \log a}\]
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