#### Question

If \[y = \log_a x, \text{ find } \frac{dy}{dx} \] ?

#### Solution

\[\text{ We have, y} = \log_a x\]

\[ \Rightarrow y = \frac{\log x}{\log a} \left[ \because \log_a b = \frac{\log b}{\log a} \right]\]

\[\Rightarrow \frac{dy}{dx} = \frac{1}{\log a}\frac{d}{dx}\left( \log x \right)\]

\[ \Rightarrow \frac{dy}{dx} = \frac{1}{\log a}\left( \frac{1}{x} \right)\]

\[ \Rightarrow \frac{dy}{dx} = \frac{1}{x \log a}\]

Is there an error in this question or solution?

Solution If Y = Log a X , Find D Y D X ? Concept: Simple Problems on Applications of Derivatives.