If \(y = e^{\log_e(\sin x)}\), where \(0 \lt x \lt \pi\), then \(\displaystyle\frac{dy}{dx}\) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\cos x\)
Since \(e^{\log_e u} = u\) for u > 0, and \(\sin x \gt 0\) for \(0 \lt x \lt \pi\), the function simplifies first:
\(y = e^{\log_e(\sin x)} = \sin x\)
So
\( \displaystyle \frac{dy}{dx} = \cos x \)