1. **Stating the problem:** Calculate the derivative of the function $f(x) = x^2 - 2x$ at the point $x_0 = 2$ using the definition of the derivative. 2. **Definition of derivative:** The derivative of a function $f(x)$ at a point $x_0$ is given by the limit $$f'(x_0) = \lim_{h \to 0} \frac{f(x_0 + h) - f(x_0)}{h}$$ This means we find the average rate of change over an interval $h$ and then let $h$ approach zero. 3. **Apply the definition:** $$f'(2) = \lim_{h \to 0} \frac{(2 + h)^2 - 2(2 + h) - (2^2 - 2 \cdot 2)}{h}$$ 4. **Simplify the numerator:** $$(2 + h)^2 - 2(2 + h) = (4 + 4h + h^2) - (4 + 2h) = 4 + 4h + h^2 - 4 - 2h = 2h + h^2$$ 5. **Substitute back:** $$f'(2) = \lim_{h \to 0} \frac{2h + h^2 - (4 - 4)}{h} = \lim_{h \to 0} \frac{2h + h^2}{h}$$ 6. **Cancel common factor $h$:** $$\frac{\cancel{h}(2 + h)}{\cancel{h}} = 2 + h$$ 7. **Take the limit as $h \to 0$:** $$f'(2) = 2 + 0 = 2$$ **Final answer:** The derivative of $f(x) = x^2 - 2x$ at $x = 2$ is $\boxed{2}$.