Answer
$g^{\prime}(x)=5 e^{5x-3}$
Work Step by Step
We have: $g(x)=e^{3x-1} e^{x-2} e^x=e^{5x-3}$
We differentiate both sides with respect to $x$.
$g^{\prime}(x)=\dfrac{d}{dx} [e^{5x-3}]$
Use rule: $\displaystyle \frac{d}{dx}[u^{n}]=nu^{n-1} \frac{du}{dx}$
Now, $g^{\prime}(x)=e^{5x-3}\dfrac{d}{dx} (5x-3)=e^{5x-3}(5)$
Simplify to obtain:
$g^{\prime}(x)=5 e^{5x-3}$
