`f(x) = (x^3 - 3x^2 +4)/(x^2)` Find the derivative of the function.

Textbook Question

Chapter 2, 2.2 - Problem 45 - Calculus of a Single Variable (10th Edition, Ron Larson).
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kalau | (Level 2) Adjunct Educator

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Divide each term by  to avoid the quotient rule.

`f(x) = x-3+4x^-2`

Take the derivative of each term. Use the power rule for the last term.

`f'(x)= 1-0+(-2)(4)(x^-3)`

`f'(x) = 1-8x^-3`

Rewrite the negative exponent as a fraction.

The answer is:

`f'(x) = 1-8/x^3`

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