#### Answer

The Derivative is:
$y'=4\sec x\tan x-\csc^2 x$

#### Work Step by Step

$y=\frac{4}{\cos x}+\frac{1}{\tan x}$
$y=4\frac{1}{\cos x}+\frac{1}{\tan x}$
$y=4\sec x+\cot x$
Applying Derivative rules:
$y'=4\frac{d}{dx}(\sec x)+\frac{d}{dx}(\cot x)$
$y'=4(\sec x\tan x)+(-\csc^2x)$
$y'=4\sec x\tan x-\csc^2 x$