Question

Find derivative of $\left[\log \left|\sec x+\tan x\right|\right]$.

Answer 1

$\frac{d}{dx}\left[\log |\sec x+\tan x|\right]$

$=\frac{1}{|\sec x+\tan x|}\frac{d}{dx}\left(|\sec x+\tan x|\right)$

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

$=\frac{1}{|\sec x+\tan x|}\left|\sec x\right||\tan x+\sec x|$

$=\left|\sec x\right|$