# How do you differentiate g(y) =(x^3 + x)(4x^2+5)  using the product rule?

Product rule states that for $y = f \left(x\right) g \left(x\right)$, then $y ' = f ' \left(x\right) g \left(x\right) + f \left(x\right) g ' \left(x\right)$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \left(3 {x}^{2} + 1\right) \left(4 {x}^{2} + 5\right) + \left({x}^{3} + x\right) \left(8 x\right)$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \left(12 {x}^{4} + 15 {x}^{2} + 4 {x}^{2} + 5\right) + \left(8 {x}^{4} + 8 {x}^{2}\right)$
$\frac{\mathrm{dy}}{\mathrm{dx}} = 20 {x}^{4} + 27 {x}^{2} + 5$