1. **State the problem:** Differentiate the function $$f(x) = x^3 - 4x + 6$$ with respect to $$x$$. 2. **Recall the differentiation rules:** - The derivative of a sum/difference is the sum/difference of the derivatives (linearity). - Power rule: $$\frac{d}{dx} x^n = nx^{n-1}$$. - Derivative of a constant is zero. 3. **Apply linearity:** $$\frac{d}{dx} (x^3 - 4x + 6) = \frac{d}{dx} (x^3) - \frac{d}{dx} (4x) + \frac{d}{dx} (6)$$ 4. **Differentiate each term:** - Using power rule: $$\frac{d}{dx} (x^3) = 3x^2$$ - Derivative of linear term: $$\frac{d}{dx} (4x) = 4$$, so contribution is $$-4$$ - Derivative of constant: $$\frac{d}{dx} (6) = 0$$ 5. **Combine results:** $$\boxed{3x^2 - 4}$$ This is the derivative of the given function, representing the slope of the tangent line at any point $$x$$.