Differentiate the following functions with respect to x: e^ - Vidyadip

Question

Differentiate the following functions with respect to x:
$\text{e}^{\tan\text{x}}$

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Answer

Let $\text{y}=\text{e}^{\tan \text{x}}$
Differentiate it with respect to x we get,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\Big(\text{e}^{\tan\text{x}}\Big)$
$=\text{e}^{\tan\text{x}}\frac{\text{d}}{\text{dx}}(\tan\text{x})$
[Using chain rule]
$=\text{e}^{\tan\text{x}}\times\sec^2\text{x} $
So, $\frac{\text{d}}{\text{dx}}\big(\text{e}^{\tan\text{x}}\big)=\sec^2\text{xe}^{\tan\text{x}}$

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