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

Core Concept

This requires the quotient rule. If f(x) = g(x)/h(x), then f'(x) = [g'(x)h(x) - g(x)h'(x)]/[h(x)]^2. Here, g(x) = 3x^2 + 2x, so g'(x) = 6x + 2. And h(x) = x^3 - 1, so h'(x) = 3x^2. Therefore, f'(x) = [(6x + 2)(x^3 - 1) - (3x^2 + 2x)(3x^2)]/(x^3 - 1)^2, which is option A. Option B is incorrect because it has a plus sign instead of a minus sign between the terms. Option C is incorrect because it doesn't square the denominator. Option D is incorrect because it has a plus sign and doesn't square the denominator.