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Question
Differentiate sin (log x) ?
Solution
\[\text{Let y} = \sin\left( \log x \right)\]
\[\text{ Differentiate it with respect to x we get }, \]
\[\frac{d y}{d x} = \frac{d}{dx}\sin\left( \log x \right)\]
\[ = \cos\left( \log x \right)\frac{d}{dx}\left( \log x \right) \left[ \text{using chain rule } \right]\]
\[ = \frac{1}{x}\cos\left( \log x \right)\]
\[So, \frac{d}{dx}\left\{ \sin\left( \log x \right) \right\} = \frac{1}{x}\cos\left( \log x \right)\]
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