1. **State the problem:** Find the derivative $\frac{dy}{dx}$ for the function $y = x - 4 - \frac{1}{x}$. 2. **Recall the derivative rules:** - The derivative of $x$ with respect to $x$ is 1. - The derivative of a constant is 0. - The derivative of $x^n$ is $nx^{n-1}$. - The derivative of $\frac{1}{x}$ can be rewritten as $x^{-1}$, so its derivative is $-1 \cdot x^{-2} = -\frac{1}{x^2}$. 3. **Apply the derivative to each term:** $$\frac{dy}{dx} = \frac{d}{dx}(x) - \frac{d}{dx}(4) - \frac{d}{dx}\left(\frac{1}{x}\right)$$ 4. **Calculate each derivative:** $$\frac{dy}{dx} = 1 - 0 - \left(-\frac{1}{x^2}\right)$$ 5. **Simplify the expression:** $$\frac{dy}{dx} = 1 + \frac{1}{x^2}$$ **Final answer:** $$\frac{dy}{dx} = 1 + \frac{1}{x^2}$$ This corresponds to option B.