1. **State the problem:** Find the derivative of the function $y = \ln(4x + 3)$.\n\n2. **Recall the formula:** The derivative of $\ln(u)$ with respect to $x$ is given by $\frac{d}{dx}[\ln(u)] = \frac{1}{u} \cdot \frac{du}{dx}$. This is an application of the chain rule.\n\n3. **Identify the inner function:** Here, $u = 4x + 3$.\n\n4. **Compute the derivative of the inner function:** $\frac{du}{dx} = 4$.\n\n5. **Apply the chain rule:**\n$$\frac{dy}{dx} = \frac{1}{4x + 3} \cdot 4 = \frac{4}{4x + 3}.$$\n\n6. **Final answer:** The derivative of $y = \ln(4x + 3)$ is\n$$\boxed{\frac{dy}{dx} = \frac{4}{4x + 3}}.$$