1. Problem: Differentiate the function $f(x) = x^6 + 2x - 1$. 2. Use the power rule for derivatives: If $f(x) = x^n$, then $f'(x) = nx^{n-1}$. 3. Differentiate each term: $$\frac{d}{dx} x^6 = 6x^5$$ $$\frac{d}{dx} 2x = 2$$ $$\frac{d}{dx} (-1) = 0$$ 4. Combine the results: $$f'(x) = 6x^5 + 2$$ This is the derivative of the first function.