1. **State the problem:** We are given the function $h = (4g + 7)^2$ and need to find the derivative $\frac{dh}{dg}$. 2. **Recall the formula:** To differentiate a function of the form $h = [u(g)]^2$, use the chain rule: $$\frac{dh}{dg} = 2u(g) \cdot \frac{du}{dg}$$ where $u(g) = 4g + 7$. 3. **Differentiate the inner function:** $$\frac{du}{dg} = \frac{d}{dg}(4g + 7) = 4$$ 4. **Apply the chain rule:** $$\frac{dh}{dg} = 2(4g + 7) \cdot 4$$ 5. **Simplify the expression:** $$\frac{dh}{dg} = 8(4g + 7)$$ 6. **Expand if desired:** $$\frac{dh}{dg} = 8 \times 4g + 8 \times 7 = 32g + 56$$ **Final answer:** $$\frac{dh}{dg} = 32g + 56$$