If f(x) = sin(3x^2), then f'(x) = ?

Core Concept

This requires the chain rule. The derivative of sin(u) is cos(u) times u', where u = 3x^2. The derivative of 3x^2 is 6x. So f'(x) = cos(3x^2) × 6x = 6x cos(3x^2), which is option B. Option A is incorrect because it doesn't include the derivative of the inner function. Option C is incorrect because it doesn't apply the chain rule properly. Option D is incorrect because it has a negative sign, which shouldn't be there.