# How do you differentiate f(x)= ( 4- secx )/ (x + 1)  using the quotient rule?

May 24, 2016

$\frac{\mathrm{df}}{\mathrm{dx}} = \frac{\sec x - 4 - \sec x \tan x \left(x + 1\right)}{x + 1} ^ 2$

#### Explanation:

According to quotient rule, if $f \left(x\right) = g \frac{x}{h \left(x\right)}$, then

$\frac{\mathrm{df}}{\mathrm{dx}} = \frac{h \left(x\right) \times g ' \left(x\right) - g \left(x\right) \times h ' \left(x\right)}{h \left(x\right)} ^ 2$

Hence as $f \left(x\right) = \frac{4 - \sec x}{x + 1}$

$\frac{\mathrm{df}}{\mathrm{dx}} = \frac{\left(x + 1\right) \left(- \sec x \tan x\right) - \left(4 - \sec x\right)}{x + 1} ^ 2$

= $\frac{\sec x - 4 - \sec x \tan x \left(x + 1\right)}{x + 1} ^ 2$