Question

Differentiate \[e^{\tan 3 x} \] ?

Answer 1

\[\text{Let y} = e^{\tan3x} \]

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

\[\frac{d y}{d x} = \frac{d}{dx}\left(e^{\tan3 x} \right)\]

\[ = e^{\tan3x} \frac{d}{dx}\left( \tan3x \right) \]

\[ = e^{\tan3x} \sec^2 3x \times \frac{d}{dx}\left( 3x \right)\]

\[ = e^{\tan3x} \sec^2 3x \times 3\]

\[So, \frac{d}{dx}\left( e^{\tan3x} \right) = 3 e^{\tan3x} \sec^2 3x\]