1. **Problem statement:** Find the derivative of the function $y = \ln(2 + \sin x)$. 2. **Recall formulas and rules:** - Derivative of $\ln(u)$ is $\frac{u'}{u}$. - Chain rule: derivative of composite function $f(g(x))$ is $f'(g(x)) \cdot g'(x)$. - Derivative of $\sin x$ is $\cos x$. 3. **Calculate derivatives step-by-step:** - Let $v = 2 + \sin x$, then $v' = \cos x$. - So, $\frac{d}{dx} \ln(2 + \sin x) = \frac{v'}{v} = \frac{\cos x}{2 + \sin x}$. 4. **Final answer:** $\boxed{\frac{dy}{dx} = \frac{\cos x}{2 + \sin x}}$