1. The problem is to find the derivative of a function and evaluate it. 2. The derivative of a function $f(x)$, denoted $f'(x)$ or $\frac{d}{dx}f(x)$, represents the rate of change or slope of the function at any point $x$. 3. The basic rules for derivatives include: - Power rule: $\frac{d}{dx} x^n = n x^{n-1}$ - Constant rule: $\frac{d}{dx} c = 0$ where $c$ is a constant - Sum rule: $\frac{d}{dx} [f(x) + g(x)] = f'(x) + g'(x)$ - Product rule: $\frac{d}{dx} [f(x) g(x)] = f'(x) g(x) + f(x) g'(x)$ - Quotient rule: $\frac{d}{dx} \left( \frac{f(x)}{g(x)} \right) = \frac{f'(x) g(x) - f(x) g'(x)}{g(x)^2}$ - Chain rule: $\frac{d}{dx} f(g(x)) = f'(g(x)) g'(x)$ 4. Since the user did not specify a particular function, let's consider a general example: $f(x) = 3x^2 + 5x - 4$. 5. Applying the power rule and constant rule: $$ f'(x) = \frac{d}{dx} (3x^2) + \frac{d}{dx} (5x) - \frac{d}{dx} (4) = 3 \cdot 2 x^{2-1} + 5 \cdot 1 x^{1-1} - 0 = 6x + 5 $$ 6. To evaluate the derivative at a specific point, say $x=2$: $$ f'(2) = 6 \cdot 2 + 5 = 12 + 5 = 17 $$ 7. Therefore, the derivative of the function $f(x) = 3x^2 + 5x - 4$ is $f'(x) = 6x + 5$, and its value at $x=2$ is 17.