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Question
Differentiate etan x ?
Solution
\[\text{Let y} = e^{\tan x} \]
\[\text{Differentiate it with respect to x we get}, \]
\[\frac{d y}{d x} = \frac{d}{dx}\left( e^{\tan x} \right)\]
\[ = e^{\tan x} \frac{d}{dx}\left( \tan x \right) \] .......[ using chain rule]
\[ = e^{\tan x} \times \sec^2 x\]
\[So, \frac{d}{dx}\left( e^{\tan x} \right) = \sec^2 x e^{\tan x}\]
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