Question

Differentiate e^tan x ?

Answer 1

\[\text{Let y} = e^{\tan x} \]

\[\text{Differentiate it with respect to x we get}, \]

\[\frac{d y}{d x} = \frac{d}{dx}\left( e^{\tan x} \right)\]

      \[ = e^{\tan x} \frac{d}{dx}\left( \tan x \right) \]   .......[ using chain rule]

      \[ = e^{\tan x} \times \sec^2 x\]

\[So, \frac{d}{dx}\left( e^{\tan x} \right) = \sec^2 x e^{\tan x}\]