Question

Differentiate $log|\tan x|+\frac{1}{2}{\tan }^{2}x+C$.

Answer 1

$\frac{d}{dx}(\log |\tan x|+\frac{1}{2}{\tan }^{2}x+c)$

$=\frac{d}{dx}(\log |+\tan x|)+\frac{d}{dx}\left(\frac{1}{2}{\tan }^{2}x\right)+\frac{d}{dx}\left(c\right)$

$=\frac{1}{|\tan x|}.\frac{d}{dx}(|\tan x|+\frac{1}{2}.2\tan x\frac{d}{dx}(\tan x)+0$

$=\frac{{\sec }^{2}x}{\tan x}+\tan x.{\sec }^{2}x$