1. **State the problem:** We are given the function $y = 7x^2 - 4$ and need to find its differential $dy$. 2. **Recall the formula:** The differential $dy$ of a function $y = f(x)$ is given by $$dy = f'(x) dx$$ where $f'(x)$ is the derivative of $f(x)$ with respect to $x$. 3. **Find the derivative:** Differentiate $y = 7x^2 - 4$ term-by-term: $$\frac{dy}{dx} = \frac{d}{dx}(7x^2) - \frac{d}{dx}(4) = 7 \cdot 2x - 0 = 14x$$ 4. **Write the differential:** Substitute $f'(x) = 14x$ into the differential formula: $$dy = 14x \, dx$$ 5. **Interpretation:** The differential $dy$ represents the approximate change in $y$ for a small change $dx$ in $x$. It is proportional to $x$ and the change $dx$. **Final answer:** $$dy = 14x \, dx$$