Find `(dy)/(dx)` if, `y=sinxsin2xsin3xsin4x`

Explanation

To find the derivative \( \frac{dy}{dx} \) for the function \( y = \sin x \sin 2x \sin 3x \sin 4x \), we can use logarithmic differentiation. Here’s a step-by-step solution:

### Step 1: Take the natural logarithm of both sides
We start by taking the natural logarithm of \( y \):
\[ \ln y = \ln(\sin x \sin 2x \sin 3x \sin 4x) \]

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