Differentiate $y = e^{\log(\sin x)}$, where $x \in (0, \pi)$, with respect to $x$.
Answer & explanation
Correct answer: option 1
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 $x$.
$\frac{dy}{dx} = \cos x$