1. **Problem Statement:** Find the derivative of the function \( w = \left(1 + \frac{3z}{3z}\right)(3 - z) \) using the product rule. 2. **Simplify the function first:** Note that \( \frac{3z}{3z} = 1 \) for \( z \neq 0 \), so the function simplifies to \( w = (1 + 1)(3 - z) = 2(3 - z) \). 3. **Rewrite the function:** \( w = 2(3 - z) = 6 - 2z \). 4. **Derivative formula:** The derivative of a product \( u(z)v(z) \) is \( u'(z)v(z) + u(z)v'(z) \). However, since the function is simplified to a linear function, we can differentiate directly. 5. **Differentiate:** \[ \frac{dw}{dz} = \frac{d}{dz}(6 - 2z) = 0 - 2 = -2 \] 6. **Interpretation:** The derivative \( w' = -2 \) means the function decreases at a constant rate of 2 with respect to \( z \). **Final answer:** \[ \boxed{\frac{dw}{dz} = -2} \]