1. **Problem:** Differentiate the function $y = 2x^2 + 3x - 20$. 2. **Formula:** The derivative of $x^n$ is given by $\frac{d}{dx} x^n = n x^{n-1}$. 3. **Step-by-step solution:** 1. Differentiate each term separately using the power rule. 2. For $2x^2$, derivative is $2 \times 2 x^{2-1} = 4x$. 3. For $3x$, derivative is $3 \times 1 x^{1-1} = 3$. 4. For constant $-20$, derivative is $0$. 4. **Combine results:** $$\frac{dy}{dx} = 4x + 3 + 0 = 4x + 3$$ 5. **Explanation:** The derivative measures the rate of change of the function. Constants vanish because they do not change with $x$. Each term's power reduces by one, and the original power multiplies the coefficient. **Final answer:** $$\boxed{\frac{dy}{dx} = 4x + 3}$$