$d / d x\left(1 / x^{3}-1 / x+x^{2}\right)$ at $x=-1$ is
(A) -6
(B) -4
(C) 0
(D) 2
(E) 6

Answer

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Answer

Final Answer: $\boxed{-4}$

Steps

Step 1 ：Given the function $f(x) = x^{2} - \frac{1}{x} + \frac{1}{x^{3}}$

Step 2 ：Find the derivative of the function, $f'(x) = 2x + \frac{1}{x^{2}} - \frac{3}{x^{4}}$

Step 3 ：Substitute $x = -1$ into the derivative, $f'(-1) = 2(-1) + \frac{1}{(-1)^{2}} - \frac{3}{(-1)^{4}} = -4$

Step 4 ：Final Answer: $\boxed{-4}$