Question

For \[x>0\], differentiate \[\sin(\log x)\] with respect to \[x\].

Options

• \[-\frac{\cos(\log x)}{x}\]

• \[\frac{\cos(\log x)}{x}\]

• \[\cos(\log x)\]

• \[\frac{\sin(\log x)}{x}\]

Answer 1

The derivative of \[\sin(\log x)\] is \[\cos(\log x)\] times the derivative of \[\log x\]. Since \[\frac{d}{dx}(\log x)=\frac{1}{x}\], the derivative is \[\frac{\cos(\log x)}{x}\].