# How do you derive y = (4x^4 − 2) / (-x^2 + 1) using the quotient rule?

Apr 9, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{16 {x}^{3} - 8 {x}^{5} - 4 x}{- {x}^{2} + 1} ^ 2$

#### Explanation:

$y = \frac{4 {x}^{4} - 2}{- {x}^{2} + 1}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\left(- {x}^{2} + 1\right) \left(16 {x}^{3}\right) - \left(4 {x}^{4} - 2\right) \left(- 2 x\right)}{- {x}^{2} + 1} ^ 2$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{- 16 {x}^{5} + 16 {x}^{3} + 8 {x}^{5} - 4 x}{- {x}^{2} + 1} ^ 2$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{16 {x}^{3} - 8 {x}^{5} - 4 x}{- {x}^{2} + 1} ^ 2$