# How do you find the derivative of f(z)=e^z(cosz)?

Apr 11, 2018

$f ' \left(z\right) = {e}^{z} \left(\cos z - \sin z\right)$

#### Explanation:

use product rule:

$f ' \left(z\right) = \frac{d}{\mathrm{dz}} \left({e}^{z}\right) \cdot \cos z + \frac{d}{\mathrm{dz}} \left(\cos z\right) \cdot {e}^{z}$

$f ' \left(z\right) = {e}^{z} \cdot \cos z - \sin z \cdot {e}^{z}$

$f ' \left(z\right) = {e}^{z} \left(\cos z - \sin z\right)$