# How do you differentiate g(z) = z^3sin(2z) using the product rule?

$g ' \left(z\right) = 2 {z}^{3} \cdot \cos \left(2 z\right) + 3 {z}^{2} \cdot \sin \left(2 z\right)$

#### Explanation:

Differentiate with respect to $z$

$g \left(z\right) = {z}^{3} \cdot \sin \left(2 z\right)$

$g ' \left(z\right) = {z}^{3} \cdot \frac{d}{\mathrm{dz}} \sin \left(2 z\right) + \sin \left(2 z\right) \cdot \frac{d}{\mathrm{dz}} \left({z}^{3}\right)$

$g ' \left(z\right) = {z}^{3} \cdot 2 \cos \left(2 z\right) + \sin \left(2 z\right) \cdot 3 {z}^{2}$

$g ' \left(z\right) = 2 {z}^{3} \cdot \cos \left(2 z\right) + 3 {z}^{2} \cdot \sin \left(2 z\right)$

God bless....I hope the explanation is useful.