If f(x) = 3x^4 - 2x^3 + 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 3x^4, we get 12x^3. For -2x^3, we get -6x^2. For 5x, we get 5. The derivative of a constant (-7) is 0. So f'(x) = 12x^3 - 6x^2 + 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.