Given the function $f(x, y) = 5x^2 y \sec(6xy)$, we can explore its various properties such as partial derivatives, critical points, or integrals depending on the context.

Let me know what you want to focus on, or if you’d like a detailed breakdown of any specific aspect!

Here are five relative questions you might want to explore further:

1. Would you like to calculate the partial derivatives of $f(x, y)$ with respect to $x$ or $y$?
2. Are you interested in determining the critical points of the function?
3. Should we explore the behavior of $f(x, y)$ for specific values of $x$ and $y$?
4. Would you like to integrate this function over a given region?
5. Are you curious about the behavior of $f(x, y)$ near points where $6xy = \frac{\pi}{2}$, where secant might be undefined?

Tip: The secant function, $\sec(\theta)$, is undefined when $\theta = \frac{\pi}{2} + n\pi$, so keep that in mind when analyzing the domain of functions involving $\sec$.