Answer
$f'(x)=3e^{3x-1}$
$f''(x)=9e^{3x-1}$
$f''(x)=27e^{3x-1}$
$f^{(4)}(x)=81e^{3x-1} $
$f^{(n)}(x)=3^{n}e^{3x-1}$
Work Step by Step
$f'''(x)=\displaystyle \frac{d}{dx}\left[f''(x)\right]$
$f^{(4)}(x)=\displaystyle \frac{d}{dx}\left[f'''(x)\right]$
$\displaystyle \quad f^{(5)}(x)=\frac{d}{dx}\left[f^{(4)}(x)\right]$
and so on, assuming all these derivatives exist.
---
$f(x)=e^{3x-1}$
$f'(x)=e^{3x-1}(3)=3e^{3x-1}$
$f''(x)=3e^{3x-1}(3)=9e^{3x-1}$
$f''(x)=9e^{3x-1}(3)=27e^{3x-1}$
$f^{(4)}(x)=27e^{3x-1}(3)=81e^{3x-1}$
$\cdots$
$f^{(n)}(x)=3^{n}e^{3x-1}$
