1. **Problem Statement:** Find the derivative of the function $f(x) = 4 \log x^3$. 2. **Rewrite the function:** Using logarithm properties, $\log x^3 = 3 \log x$, so $$f(x) = 4 \cdot 3 \log x = 12 \log x.$$ 3. **Recall the derivative formula:** The derivative of $\log x$ (logarithm base 10) is $$\frac{d}{dx} \log x = \frac{1}{x \ln 10}.$$ 4. **Apply the derivative:** $$f'(x) = 12 \cdot \frac{1}{x \ln 10} = \frac{12}{x \ln 10}.$$ 5. **Interpretation:** None of the given options exactly match this derivative. **Final answer:** The derivative is $f'(x) = \frac{12}{x \ln 10}$, so the correct choice is (a) None of them.