Final answer:
The derivative of the function f(x) = 2/x^3 - 5/x^2 - 1/x + 450 is f'(x) = -6/x^4 + 10/x^3 + 1/x^2.
Step-by-step explanation:
The student has asked to find the derivative of the following function:
f(x) = \frac{2}{x^3} - \frac{5}{x^2} - \frac{1}{x} + 450.
To find the derivative, we will apply the power rule to each term where the power rule states that the derivative of x^n is n \cdot x^{n-1}. The derivative of a constant is zero. Thus:
f'(x) = -6 \cdot x^{-4} + 10 \cdot x^{-3} + 1 \cdot x^{-2} + 0,
which simplifies to:
f'(x) = -6/x^4 + 10/x^3 + 1/x^2.
We used the rules of differentiation to find the answer step by step.