The given function is:

$f(x) = 3xe^x - e^{2x}$

Would you like me to differentiate this function, find its critical points, or perform another operation on it? Let me know how you'd like to proceed.

Here are five possible questions related to this problem:

1. Would you like to find the derivative $f'(x)$?
2. Do you want to determine the critical points of $f(x)$?
3. Should we explore the concavity and inflection points of $f(x)$?
4. Do you need to find the limits of $f(x)$ as $x$ approaches infinity or negative infinity?
5. Would you like to solve $f(x) = 0$ to find the x-values where the function is zero?

Tip: The product and chain rules are essential for differentiating functions like $f(x) = 3xe^x - e^{2x}$.