# How do you find the derivative of f(x) = (x^3-3x^2+4)/x^2?

Jun 9, 2016

$\frac{d}{\mathrm{dx}} f \left(x\right) = 1 - \frac{8}{x} ^ 3$

#### Explanation:

Divide, then use the power rule...

$\frac{d}{\mathrm{dx}} f \left(x\right)$

$= \frac{d}{\mathrm{dx}} \frac{{x}^{3} - 3 {x}^{2} + 4}{x} ^ 2$

$= \frac{d}{\mathrm{dx}} \left(x - 3 + 4 {x}^{- 2}\right)$

$= 1 - 8 {x}^{- 3}$

$= 1 - \frac{8}{x} ^ 3$