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

Nov 2, 2015

Use the product rule of differentiation to eventually obtain $5 {x}^{4} + 8 x$

#### Explanation:

According to the product rule, $\frac{d}{\mathrm{dx}} \left[f \left(x\right) \cdot g \left(x\right)\right] = f \left(x\right) \cdot g ' \left(x\right) + g \left(x\right) \cdot f ' \left(x\right)$

So applying it in this case we get

$\frac{d}{\mathrm{dx}} \left[\left({x}^{2}\right) \left({x}^{3} + 4\right)\right] = {x}^{2} \cdot 3 {x}^{2} + \left({x}^{3} + 4\right) \cdot 2 x$

$= 5 {x}^{4} + 8 x$