Differentiate log sin x w.r.t. `sqrt(x).`

Explanation

To differentiate \( \log(\sin x) \) with respect to \( \sqrt{x} \), we will use the chain rule and the concept of derivatives. Here’s a step-by-step solution:

### Step 1: Define the functions
Let:
- \( u = \log(\sin x) \)
- \( v = \sqrt{x} \)

### Step 2: Differentiate \( u \) with respect to \( x \)
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