1. **Problem Statement:** Find the derivative of a function $f(x)$ using the basic rules of calculus. 2. **Formula Used:** The derivative of a function $f(x)$ is given by the limit definition: $$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$ 3. **Important Rules:** - The derivative of $x^n$ is $nx^{n-1}$. - The derivative of a constant is 0. - The derivative of a sum is the sum of the derivatives. 4. **Example:** Suppose $f(x) = x^2$. 5. **Intermediate Work:** Using the power rule: $$f'(x) = 2x^{2-1} = 2x$$ 6. **Explanation:** The derivative $f'(x)$ represents the rate of change or slope of the function $f(x)$ at any point $x$. For $f(x) = x^2$, the slope at any $x$ is $2x$. 7. **Final Answer:** $$f'(x) = 2x$$