# What is the derivative of cos^7(e^x)?

Jun 6, 2018

$y ' = 7 {\cos}^{6} \left({e}^{x}\right) \left(- \sin \left({e}^{x}\right)\right) \cdot {e}^{x}$

#### Explanation:

By the power and the chain rule we get

$y ' = 7 {\cos}^{7 - 1} \cdot \left(- \sin \left({e}^{x}\right)\right) \cdot {e}^{x}$
since
$\left(\cos \left(x\right)\right) ' = - \sin \left(x\right)$
$\left({e}^{x}\right) ' = {e}^{x}$