Correct option is (B) \(\sec x\)
Given,
\(\frac{d}{d x}(\log (\sec x+\tan x))\)
\(\frac{{d} y}{{~d} x} =\frac{1}{(\sec x+\tan x)} \times \frac{d}{d x}(\sec x+\tan x) \)
\( =\left[\frac{1}{(\sec x+\tan x)}\right] \times\left(\sec x \tan x+\sec ^2 x\right) \)
\(=\left[\frac{1}{(\sec x+\tan x)}\right] \times \sec x(\tan x+\sec x)\)
\(=\sec x\)