Final answer:
The derivative of the function f(x) = x⁶ - 1 - 6x⁸ is 6x⁵ - 48x⁷.
Step-by-step explanation:
To find the derivative of the function f(x) = x⁶ - 1 - 6x⁸, we can differentiate each term separately. The derivative of x⁶ is 6x⁵, the derivative of 1 is 0, and the derivative of 6x⁸ is 48x⁷. Adding these derivatives together, we get the derivative of f(x) as 6x⁵ - 48x⁷.