# What is the derivative of (x^3-3x^2+4)/x^2?

May 8, 2016

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

#### Explanation:

Divide each term on the numerator by ${x}^{2}$

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

now differentiating using the $\textcolor{b l u e}{\text{ power rule }}$

$\Rightarrow \frac{d}{\mathrm{dx}} \left(x - 3 + 4 {x}^{-} 2\right) = 1 - 8 {x}^{-} 3 = 1 - \frac{8}{x} ^ 3$