1. The problem asks to find the derivative with respect to $x$ of the function $a^3 \log_a x$. 2. Recall the formula for the derivative of $\log_a x$: $$\frac{d}{dx} \log_a x = \frac{1}{x \ln a}$$ where $a > 0$ and $a \neq 1$. 3. The function is $y = a^3 \log_a x$. Since $a^3$ is a constant with respect to $x$, we can write: $$\frac{dy}{dx} = a^3 \cdot \frac{d}{dx} \log_a x = a^3 \cdot \frac{1}{x \ln a}$$ 4. Therefore, the derivative is: $$\frac{dy}{dx} = \frac{a^3}{x \ln a}$$ 5. Now, let's check the options given: (A) $-\frac{2}{x^3}$ (B) $-\frac{3}{x^3}$ (C) $-\frac{3}{x^4}$ (D) $3x^2$ None of these match the derivative we found. However, since the problem is multiple choice, and the function involves $a^3 \log_a x$, the derivative is $\frac{a^3}{x \ln a}$. 6. If $a= e$, then $\ln a = 1$ and the derivative simplifies to $\frac{e^3}{x}$, but this is not among the options. 7. Since none of the options match the correct derivative, the correct derivative is $\frac{a^3}{x \ln a}$. Final answer: $\boxed{\frac{a^3}{x \ln a}}$