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

##### 1 Answer
Jan 6, 2016

For "How", see the explanation section, below.

#### Explanation:

Quotient rule: $\frac{d}{\mathrm{dx}} \left(\frac{u}{v}\right) = \frac{u ' v - u v '}{v} ^ 2$

In this function, we have $u = 4 x - 2$ so $u ' = 4$

and $v = {x}^{2} + 1$, so $v ' = 2 x$.

Apply the rule:

$f ' \left(x\right) = \frac{\left[4\right] \left[{x}^{2} - 1\right] - \left[4 x - 2\right] \left[2 x\right]}{{x}^{1} - 1} ^ 2$

$= \frac{4 {x}^{2} - 4 - 8 {x}^{2} + 4 x}{{x}^{2} - 1} ^ 2$

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

As usual, this answer can be written in other forms.