Question

If $y=e^{\sin \left(\log x\right)}$, then $\frac{dy}{dx}=$

• A. $e^{\cos \left(\log x\right)}$
• B. $\frac{y}{x}\cos \left(\log x\right)$
• C. $-\sin \left(\log x\right)$
• D. None of these

Answer 1

The correct option is B $\frac{y}{x}\cos \left(\log x\right)$

$y=e^{\sin \left(\log x\right)}$

$\frac{dy}{dx}=e^{\sin \left(\log x\right)}.\cos \left(\log x\right).\frac{1}{x}$

$\frac{dy}{dx}=\frac{y}{x}.\cos \left(\log x\right)$