# How do you differentiate g(y) =(x^2 + 6)(x^2 - 1)  using the product rule?

Jan 6, 2016

$2 x \left(2 {x}^{2} + 5\right)$
The product rule states that if $h \left(x\right) = f \left(x\right) g \left(x\right)$ then $h ' \left(x\right) = f ' \left(x\right) g \left(x\right) + f \left(x\right) g ' \left(x\right)$
$\therefore \frac{d}{\mathrm{dx}} g \left(y\right) = \left(\frac{d}{\mathrm{dx}} \left({x}^{2} + 6\right)\right) \left({x}^{2} - 1\right) + \left({x}^{2} + 6\right) \frac{d}{\mathrm{dx}} \left({x}^{2} - 1\right)$
$= 2 x \left({x}^{2} - 1\right) + \left({x}^{2} + 6\right) \cdot 2 x$
$= 2 {x}^{3} - 2 x + 2 {x}^{3} + 12 x$
$= 4 {x}^{3} + 10 x$
$= 2 x \left(2 {x}^{2} + 5\right)$