1. **Problem:** Find the derivative of $f(x) = 2x^3 - 5x^2$. 2. **Formula:** The derivative of $x^n$ is given by $\frac{d}{dx} x^n = nx^{n-1}$. 3. **Step-by-step:** - Differentiate each term separately: $$\frac{d}{dx} (2x^3) = 2 \cdot 3x^{3-1} = 6x^2$$ $$\frac{d}{dx} (-5x^2) = -5 \cdot 2x^{2-1} = -10x$$ 4. **Combine results:** $$f'(x) = 6x^2 - 10x$$ 5. **Explanation:** We apply the power rule to each term, multiply the coefficient by the exponent, then reduce the exponent by one. Final answer: $f'(x) = 6x^2 - 10x$