If `y=e^(x) log (sin 2x),` find `(dy)/(dx)`.

Explanation

To differentiate the function \( y = e^x \log(\sin(2x)) \), we will use the product rule of differentiation. The product rule states that if you have two functions \( u \) and \( v \), then the derivative \( \frac{d(uv)}{dx} = u \frac{dv}{dx} + v \frac{du}{dx} \).

### Step-by-step solution:

1. **Identify the functions**:
Let \( u = e^x \) and \( v = \log(\sin(2x)) \).

2. **Differentiate \( u \)**:
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