It looks like you're defining a function $f(x, y)$ but the format seems a bit unclear. Let's clarify and correct it.

If you intended to define a function $f(x, y)$ and you have an expression involving $y$ and $x$, it might look something like this:

$f(x, y) = y \cdot (e^{x^2} - 4x + 3)$

Is this what you meant? If not, please provide more details or correct any mistakes.

Would you like to see the steps on how to derive or analyze this function?

Here are five questions you might want to ask:

1. How do I find the partial derivatives of $f(x, y)$?
2. Can you help me evaluate $f(x, y)$ for specific values of $x$ and $y$?
3. What is the domain and range of $f(x, y)$?
4. How do I find the critical points of $f(x, y)$?
5. Can you graph the function $f(x, y)$?

Tip: When defining functions, be clear about each variable and the operations applied to them for better understanding and analysis.