Differentiate $y = e^{\log(\sin x)}$, where $x \in (0, \pi)$, with respect to $x$.

$\cos x$

The correct answer is Option (1) → $\cos x$ ##

To differentiate $y = e^{\log(\sin x)}$ with respect to $x$, where $x \in (0, \pi)$, let's simplify the expression first and then differentiate.

Use the property $e^{\log(a)} = a$, so:

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

Now we have:

$y = \sin x$

Differentiate $y = \sin x$ with respect to $x$.

$\frac{dy}{dx} = \cos x$