Final answer:
The derivative of h(x) = 4x⁴ - 2x³ + 6x² - 3x + 1 is h'(x) = 16x³ - 6x² + 12x - 3.
Step-by-step explanation:
The given function is h(x) = 4x⁴ - 2x³ + 6x² - 3x + 1. To find the derivative of h(x), we differentiate each term with respect to x. Using the power rule, the derivative of xⁿ is nxⁿ⁻¹, where n is a constant.
Therefore, the derivative of h(x) = 4x⁴ - 2x³ + 6x² - 3x + 1 is:
h'(x) = 16x³ - 6x² + 12x - 3.