# How do you differentiate f(x)=cosx/tanx using the quotient rule?

$f ' \left(x\right) = \frac{\left(- \sin x\right) \left(\tan x\right) - \left(\cos x\right) \left({\sec}^{2} x\right)}{\tan} ^ 2 x$
$f ' \left(x\right) = \frac{\left(- \sin x\right) \left(\tan x\right) - \left(\cos x\right) \left({\sec}^{2} x\right)}{\tan} ^ 2 x$
$f \left(x\right) = \cos \frac{x}{\tan} x = {\cos}^{2} \frac{x}{\sin} x = \cos x \cot x$