# How do you differentiate f(x)= ( x + 1 )/ ( secx ) using the quotient rule?

Apr 11, 2017

$f ' \left(x\right) = \frac{1 - \left(x + 1\right) \tan x}{\sec x}$

#### Explanation:

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

By factoring out $\sec x$ from the numerator,

$= \frac{\sec x \left(1 - \left(x + 1\right) \tan x\right)}{{\sec}^{2} x}$

By cancelling $\sec x$,

$= \frac{1 - \left(x + 1\right) \tan x}{\sec x}$

I hope that this was clear.