If y=2x+tanx, find y''' third derivative of y?

Apr 9, 2017

$y ' ' ' = 4 {\sec}^{2} x {\tan}^{2} x + 2 {\sec}^{4} x$

Explanation:

As $y = 2 x + \tan x$

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

• differentiating both separately

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

• differential of constant term is $0$ and using chain rule.

$y ' ' ' = 2 \left(2 {\sec}^{2} x \tan x\right) \tan x + 2 {\sec}^{2} x \left({\sec}^{2} x\right)$

$= 4 {\sec}^{2} x {\tan}^{2} x + 2 {\sec}^{4} x$