# How do you differentiate g(y) = (x^2 - 1) (4x^6 + 5)  using the product rule?

$g ' \left(x\right) = 2 x \left(4 {x}^{6} + 5\right) + 24 {x}^{5} \left({x}^{2} - 1\right)$
$g$ is the product of two functions $u$ & $v$ with $u \left(x\right) = {x}^{2} - 1$ & $v \left(x\right) = 4 {x}^{6} + 5$
So the derivative of $g$ is $u ' v + u v '$ with $u ' \left(x\right) = 2 x$ & $v ' \left(x\right) = 24 {x}^{5}$.