1. **Problem:** Differentiate the function \(g(x) = (x^2 - 2)(2x + 3)\). 2. **Formula:** Use the product rule for differentiation: \(\frac{d}{dx}[u(x)v(x)] = u'(x)v(x) + u(x)v'(x)\). 3. **Step 1:** Identify \(u(x) = x^2 - 2\) and \(v(x) = 2x + 3\). 4. **Step 2:** Differentiate each: \[u'(x) = 2x, \quad v'(x) = 2\] 5. **Step 3:** Apply the product rule: \[g'(x) = u'(x)v(x) + u(x)v'(x) = 2x(2x + 3) + (x^2 - 2)(2)\] 6. **Step 4:** Expand terms: \[2x(2x + 3) = 4x^2 + 6x\] \[(x^2 - 2)(2) = 2x^2 - 4\] 7. **Step 5:** Combine like terms: \[g'(x) = 4x^2 + 6x + 2x^2 - 4 = (4x^2 + 2x^2) + 6x - 4 = 6x^2 + 6x - 4\] **Final answer:** \(\boxed{g'(x) = 6x^2 + 6x - 4}\)