Problem

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

Solution

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: \(\boxed{-4}\)

From Solvely APP
Source: https://solvelyapp.com/problems/XUpA9KaZg6/

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