1. The problem is to find the basic derivative of a function, which is usually the easiest starting point in calculus. 2. The formula for the derivative of a function $f(x)$ is given by: $$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$ This formula represents the rate of change or slope of the function at any point $x$. 3. Important rules for derivatives include: - The derivative of a constant is 0. - The power rule: $\frac{d}{dx} x^n = n x^{n-1}$. - The sum rule: derivative of a sum is the sum of derivatives. 4. Example: Find the derivative of $f(x) = 3x^2 + 5x - 4$. 5. Apply the power rule to each term: $$\frac{d}{dx} 3x^2 = 3 \times 2 x^{2-1} = 6x$$ $$\frac{d}{dx} 5x = 5$$ $$\frac{d}{dx} (-4) = 0$$ 6. Combine the results: $$f'(x) = 6x + 5 + 0 = 6x + 5$$ 7. This derivative tells us the slope of the curve $f(x)$ at any point $x$. This is a simple and fundamental derivative problem to start your exam confidently.