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

Feb 14, 2017

$2 + \frac{3}{x} ^ 2$

#### Explanation:

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

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

$= 2 x + 1 - 3 {x}^{-} 1$

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

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\frac{d}{\mathrm{dx}} \left(a {x}^{n}\right) = n a {x}^{n - 1}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

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

$= 2 + 3 {x}^{-} 2$

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