Question

Differentiate sin (log x) ?

Answer 1

\[\text{Let y} = \sin\left( \log x \right)\]

\[\text{ Differentiate it with respect to x we get }, \]

\[\frac{d y}{d x} = \frac{d}{dx}\sin\left( \log x \right)\]

  \[ = \cos\left( \log x \right)\frac{d}{dx}\left( \log x \right) \left[ \text{using chain rule } \right]\]

   \[ = \frac{1}{x}\cos\left( \log x \right)\]

\[So, \frac{d}{dx}\left\{ \sin\left( \log x \right) \right\} = \frac{1}{x}\cos\left( \log x \right)\]