If f(x) = (2x + 1)(x^2 - 3), then f'(x) = ?

Core Concept

We can solve this using the product rule. If f(x) = g(x) × h(x), then f'(x) = g'(x) × h(x) + g(x) × h'(x). Here, g(x) = 2x + 1, so g'(x) = 2. And h(x) = x^2 - 3, so h'(x) = 2x. Therefore, f'(x) = 2(x^2 - 3) + (2x + 1)(2x) = 2x^2 - 6 + 4x^2 + 2x = 6x^2 + 2x - 6. Alternatively, we could first expand f(x) = 2x^3 - 6x + x^2 - 3 = 2x^3 + x^2 - 6x - 3, then take the derivative to get f'(x) = 6x^2 + 2x - 6. Option D is the correct answer. Option A is incorrect because it has -3 instead of -6. Option B is incorrect because it has -9 instead of -6. Option C is incorrect because it has +3 instead of -6.