# How do you differentiate f(x)=1/sec(e^(x) )  using the chain rule?

Feb 24, 2016

Use trigonometry first, then the derivative of the cosine and the chain rule.

#### Explanation:

$f \left(x\right) = \frac{1}{\sec \left({e}^{x}\right)} = \cos \left({e}^{x}\right)$

$f ' \left(x\right) = - \sin \left({e}^{x}\right) \frac{d}{\mathrm{dx}} \left({e}^{x}\right)$

$= - \sin \left({e}^{x}\right) \left({e}^{x}\right)$

$= - {e}^{x} \sin \left({e}^{x}\right)$