# How do you use the product rule to differentiate y = (x^2 + 2) (x^3 + 4)?

##### 1 Answer
May 15, 2015

If we consider the definition of product rule for the function $y = f \left(x\right) \cdot g \left(x\right)$, we have $\frac{\mathrm{dy}}{\mathrm{dx}} = f ' \left(x\right) g \left(x\right) + f \left(x\right) g ' \left(x\right)$.

Applying such concept to your function, we have

$y = 2 x \left({x}^{3} + 4\right) + \left({x}^{2} + 2\right) 3 {x}^{2}$

Simplifying:

$y = 2 {x}^{4} + 8 x + 3 {x}^{4} + 6 {x}^{2}$

$y = 5 {x}^{4} + 6 {x}^{2} + 8 x$