Differentiate the following functions with respect to x: e^ 3x - Vidyadip

Question

Differentiate the following functions with respect to x:
$\text{e}^{\tan3\text{x}}$

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Answer

Let, $\text{y}=\text{e}^{\tan3\text{x}}$
Differentiate with respect to x,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\big(\text{e}^{\tan3\text{x}}\big)$
$=\text{e}^{\tan3\text{x}}\frac{\text{d}}{\text{dx}}(\tan3\text{x})$
[Using chain rule]
$\text{e}^{\tan3\text{x}}\times\sec^23\text{x}\times\frac{\text{d}}{\text{dx}}(3\text{x})$
So,
$\frac{\text{d}}{\text{dx}}\big(\text{e}^{\tan3\text{x}}\big)=3\text{e}^{\tan3\text{x}}\times\sec^2 3\text{x}$

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