You have the function:

$f(x) = \ln(x^3 - 4x) \cdot \tan(2x)$

If you want to differentiate this function, find critical points, or analyze behavior, let me know the specifics of what you'd like to explore with this function.

Would you like a detailed breakdown, and if so, what aspect of the function would you like to focus on (e.g., differentiation, domain, etc.)?

Here are 5 questions related to the function:

1. What is the derivative of $f(x) = \ln(x^3 - 4x) \cdot \tan(2x)$?
2. What is the domain of the function?
3. How do you find the critical points of this function?
4. What happens to the function as $x \to \infty$?
5. Can you plot the behavior of this function?

Tip: When differentiating products of functions, remember to use the product rule, as well as chain rule and derivative rules for logarithmic and trigonometric functions.