If f(x) = 3x⁴ - 2x³ + 5x - 7, then f'(x) = ?

Core Concept

Using the power rule for differentiation, we bring down the exponent and multiply it by the coefficient, then reduce the exponent by 1 for each term. For 3x⁴, we get 12x³. For -2x³, we get -6x². For 5x, we get 5. The derivative of a constant (-7) is 0. So f'(x) = 12x³ - 6x² + 5, which is option A. Option B is incorrect because it has an extra x in the last term. Option C is incorrect because it has a negative sign for the last term. Option D is incorrect because it doesn't apply the power rule correctly.