1. **State the problem:** Given the function $y = \frac{7}{x}$, find the derivative $\frac{dy}{dx}$. 2. **Recall the formula:** The derivative of $y = x^n$ is $\frac{dy}{dx} = nx^{n-1}$. 3. **Rewrite the function:** Express $y$ as $y = 7x^{-1}$ to apply the power rule. 4. **Apply the power rule:** $$\frac{dy}{dx} = 7 \cdot (-1) x^{-1-1} = -7x^{-2}$$ 5. **Simplify the expression:** $$\frac{dy}{dx} = -\frac{7}{x^2}$$ 6. **Interpretation:** The derivative $\frac{dy}{dx}$ tells us the rate of change of $y$ with respect to $x$. Here, it decreases as $x$ increases, and the negative sign indicates the function is decreasing. **Final answer:** $$\frac{dy}{dx} = -\frac{7}{x^2}$$