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

Nov 1, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = 3 {x}^{2} + 6$
$y = x \left({x}^{2} + 6\right)$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \left[x \left(2 x\right) + \left({x}^{2} + 6\right) \left(1\right)\right]$
$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 {x}^{2} + {x}^{2} + 6$
$\frac{\mathrm{dy}}{\mathrm{dx}} = 3 {x}^{2} + 6$