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

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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:
$$
\frac{dy}{dx} = 3 \cot x
$$
The derivative of $$ y = 3 \ln(\sin x) $$ with respect to $$ x $$ is $$ \frac{dy}{dx} = 3 \cot x $$.

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

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