What is $\frac{d}{dx}\left(\log{\left(\tan x + \sec x \right)}\right)$ for $0 < x < \frac{\pi}{2}$?

Explanation

1. 01

   $\frac{u'}{u}$ with $u = \sec x + \tan x$, $u' = \sec x\tan x + \sec^{2} x = \sec x(\tan x + \sec x)$.

2. 02

   $\frac{\sec x(\sec x + \tan x)}{\sec x + \tan x} = \sec x$.