1. **State the problem:** Differentiate the function $f(x) = \ln(x^3 e^{3x})$ with respect to $x$ without using the Chain Rule or Product Rule. 2. **Rewrite the function using logarithm properties:** Recall that $\ln(ab) = \ln a + \ln b$. So, $$\ln(x^3 e^{3x}) = \ln(x^3) + \ln(e^{3x})$$ 3. **Simplify each logarithm:** Using $\ln(x^3) = 3\ln x$ and $\ln(e^{3x}) = 3x$, we get $$3\ln x + 3x$$ 4. **Differentiate term-by-term:** - The derivative of $3\ln x$ is $3 \cdot \frac{1}{x} = \frac{3}{x}$. - The derivative of $3x$ is $3$. 5. **Combine the derivatives:** $$\frac{3}{x} + 3$$ **Final answer:** $$\frac{d}{dx} \ln(x^3 e^{3x}) = \frac{3}{x} + 3$$