# How do you differentiate g(y) =x(x^2 - 1)  using the product rule?

Mar 4, 2017

$\frac{\mathrm{dg}}{\mathrm{dx}} = 3 {x}^{2} - 1$

#### Explanation:

Although we can use the product rule, it is easier to multiply out:

Method 1 - Product Rule

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

Method 2 - Multiply Out

$g \left(y\right) = {x}^{3} - x$
$\frac{\mathrm{dg}}{\mathrm{dx}} = 3 {x}^{2} - 1$