Find the derivative of \( y \) with respe \( y=3 \ln (\sin x) \) \( \frac{d y}{d x}=\square \)

1. Write the function: \[ y = 3 \ln(\sin x) \] 2. Differentiate using the chain rule: \[ \frac{dy}{dx} = 3 \cdot \frac{d}{dx} \Bigl[ \ln(\sin x) \Bigr] \] 3. Differentiate \(\ln(\sin x)\) by applying the chain rule: \[ \frac{d}{dx} \Bigl[ \ln(\sin x) \Bigr] = \frac{1}{\sin x} \cdot \frac{d}{dx} [\sin x] = \frac{\cos x}{\sin x} \] 4. Substitute back into the differentiated equation: \[ \frac{dy}{dx} = 3 \cdot \frac{\cos x}{\sin x} \] 5. Recognize that \(\frac{\cos x}{\sin x} = \cot x\): \[ \frac{dy}{dx} = 3 \cot x \] Thus, the final answer is: \[ \frac{dy}{dx} = 3 \cot x \]