Since the question was tagged with calculus and since it has not indicated what needs to be solved, I assume that you may need to evaluate the first order derivative, hence, you need to differentiate the function with respect to x, such that:

`f'(x) = (-x^4 - 2x^3 + 6x - 4)' => f'(x) = -4x^3 - 6x^2 + 6`

**Hence, evaluating the first order derivative of the given polynomial function, yields `f'(x) = -4x^3 - 6x^2 + 6` .**