Problem

Calculate the derivative of the rational function \(f(x) = \frac{x^3 - 2x^2 + 1}{x^2} \)

Answer

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Answer

Step 3: Simplify the derivative: \(f'(x) = 1 - \frac{2}{x^3}\)

Steps

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

Step 2 ：Step 2: Take the derivative of each term: \(f'(x) = 1 - 0 - \frac{2}{x^3}\)

Step 3 ：Step 3: Simplify the derivative: \(f'(x) = 1 - \frac{2}{x^3}\)

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