1. **State the problem:** Find the derivative of a function $f(x)$. Since the function is not specified, let's consider a general approach. 2. **Formula used:** The derivative of a function $f(x)$ is defined as $$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$ This formula gives the instantaneous rate of change of the function at any point $x$. 3. **Rules to remember:** - The derivative of a constant is 0. - The derivative of $x^n$ is $nx^{n-1}$. - The derivative of a sum is the sum of the derivatives. - The derivative of a product uses the product rule. - The derivative of a quotient uses the quotient rule. - The derivative of a composite function uses the chain rule. 4. **Example:** If $f(x) = x^2$, then $$f'(x) = 2x$$ 5. **Explanation:** The derivative tells us how fast $f(x)$ changes as $x$ changes. For $x^2$, the slope at any point $x$ is $2x$. Since the function was not specified, this is the general method to find derivatives.