1. **Problem:** Find the derivative $\frac{dy}{dx}$ for $y = \log_4 (3x - 4)$. 2. **Formula and rules:** The derivative of $y = \log_a u$ is given by $$\frac{dy}{dx} = \frac{1}{u \ln a} \cdot \frac{du}{dx}$$ where $a$ is the base of the logarithm and $u$ is a function of $x$. 3. **Identify components:** Here, $a = 4$ and $u = 3x - 4$. 4. **Find $\frac{du}{dx}$:** $$\frac{du}{dx} = \frac{d}{dx}(3x - 4) = 3$$ 5. **Apply the formula:** $$\frac{dy}{dx} = \frac{1}{(3x - 4) \ln 4} \cdot 3 = \frac{3}{(3x - 4) \ln 4}$$ 6. **Final answer:** $$\boxed{\frac{dy}{dx} = \frac{3}{(3x - 4) \ln 4}}$$