Find `dy/dx` if y= `(5x)^(3cos 2x)`

Explanation

To find \( \frac{dy}{dx} \) for the function \( y = (5x)^{3 \cos(2x)} \), we will 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 both sides of the equation:

\[ \ln y = \ln((5x)^{3 \cos(2x)}) \]
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