# How do you differentiate f(x)=secx using the quotient rule?

Nov 29, 2017

$f ' \left(x\right) = \sec x \tan x$

#### Explanation:

$f \left(x\right) = \sec x$
$= \frac{1}{\cos} x$
$f ' \left(x\right) = \frac{\left[1\right] ' \cdot \cos x - \left[\cos x\right] ' \cdot 1}{\cos} ^ 2 x$
$= \frac{0 \cdot \cos x - \left(- \sin x\right) \cdot 1}{\cos} ^ 2 x$
$= \frac{0 + \sin x}{\cos} ^ 2 x$
$= \sin \frac{x}{\cos} ^ 2 x$
$= \sin \frac{x}{\cos} x \cdot \frac{1}{\cos} x$
$= \frac{1}{\cos} x \cdot \sin \frac{x}{\cos} x$
$= \sec x \cdot \tan x$
$= \sec x \tan x$

Hope that helps.