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

Mar 16, 2016

$2 - \frac{6}{x} ^ 3$

#### Explanation:

You could differentiate this function using the ' Quotient rule ' but probably 'easier' to divide each term by ${x}^{2}$

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

which simplifies to : $2 x - 4 + 3 {x}^{-} 2$

$\Rightarrow \frac{d}{\mathrm{dx}} \left(2 x - 4 + 3 {x}^{-} 2\right) = 2 - 6 {x}^{-} 3 = 2 - \frac{6}{x} ^ 3$