Final answer:
The derivative of the function f(x) = -8x² is f'(x) = -16x, and at the point a, the derivative is f'(a) = -16a.
Step-by-step explanation:
The student has provided a function f(x) = x² - 9x², which simplifies to f(x) = -8x². The derivative of this function at any point a can be found using the power rule of differentiation. The power rule states that if f(x) = ax^n, the derivative f'(x) = nax^(n-1). Applying this rule, the derivative of f(x) = -8x² is f'(x) = -16x. Therefore, the derivative at point a is f'(a) = -16a.