# Question #f5e26

Oct 14, 2017

$y ' ' = 2 \tan x {\sec}^{2} x$

#### Explanation:

let $y = x + \tan x$.

Using the fact that the derivative of $\tan x$ is ${\sec}^{2} x$:

$y = 1 + {\sec}^{2} x$

Using the chain rule to differentiate ${\sec}^{2} x$, and the fact that the derivative of $\sec x$ is $\sec x \tan x$:

$y ' ' = 2 \sec x \times \tan x \sec x$

$\therefore y ' ' = 2 \tan x {\sec}^{2} x$