# How do you differentiate (x^2-5x+2)/root3x?

Oct 14, 2015

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{5 {x}^{\frac{2}{3}} + 10 {x}^{- \frac{5}{6}} + 2 {x}^{- \frac{4}{3}}}{3}$

#### Explanation:

The simplest way is to put the function into exponential notation, foil them and then derivate

$y = \frac{{x}^{2} - 5 x + 2}{\sqrt[3]{x}}$

$y = \left({x}^{2} - 5 x + 2\right) \cdot \left({x}^{- \frac{1}{3}}\right)$

$y = {x}^{2 - \frac{1}{3}} - 5 {x}^{1 - \frac{1}{3}} + 2 {x}^{- \frac{1}{3}}$

$y = {x}^{\frac{5}{3}} - 5 {x}^{- \frac{2}{3}} + 2 {x}^{- \frac{1}{3}}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{5 {x}^{\frac{2}{3}}}{3} - \frac{5 \cdot \left(- 2\right) \cdot {x}^{- \frac{5}{6}}}{3} + \frac{2 {x}^{- \frac{4}{3}}}{3}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{5 {x}^{\frac{2}{3}} + 10 {x}^{- \frac{5}{6}} + 2 {x}^{- \frac{4}{3}}}{3}$