1. The problem is to find the derivative of a function using basic derivative rules. 2. The basic derivative rules include: - Power rule: $$\frac{d}{dx} x^n = n x^{n-1}$$ - Constant multiple rule: $$\frac{d}{dx} [c f(x)] = c \frac{d}{dx} f(x)$$ - Sum rule: $$\frac{d}{dx} [f(x) + g(x)] = \frac{d}{dx} f(x) + \frac{d}{dx} g(x)$$ 3. Example problem: Find the derivative of $$f(x) = 3x^4 - 5x^2 + 6x - 7$$. 4. Apply the power rule and constant multiple rule to each term: $$\frac{d}{dx} 3x^4 = 3 \cdot 4 x^{4-1} = 12x^3$$ $$\frac{d}{dx} (-5x^2) = -5 \cdot 2 x^{2-1} = -10x$$ $$\frac{d}{dx} 6x = 6 \cdot 1 x^{1-1} = 6$$ $$\frac{d}{dx} (-7) = 0$$ 5. Combine the derivatives: $$f'(x) = 12x^3 - 10x + 6$$ 6. This is the derivative of the function using basic derivative rules. Final answer: $$f'(x) = 12x^3 - 10x + 6$$