given that f(x) = x^4 + 2x, find f'(x)

This is a simple differentiation question where we just differentiate by taking the power of the x and bringing that in front as a constant and then taking 1 off the power. So for the first term, x^4, we bring the 4 to the front and take 1 away from the power of the x which then becomes 3 so we get 4x^3. For the second term, 2x, the power on the x is just 1 so the constant in front, 2, remains the same and the power on the x becomes 0 since we take 1 away from it. Anything to the power of 0 is simply 1 so the second term becomes 2.Therefore, our final answer is simply 4x^3 +2