It appears that you've uploaded a mathematical problem. Let's take a look at the content:

You provided four functions in a language that seems to be Mongolian. Here's the translation of the functions:

1. $f(x, y) = e^{-x^2}(y^2 + 1)$
2. $f(x, y) = y^2 + x^2y + x^2 - 2y$
3. $f(x, y) = \tan(xy)$
4. $f(x, y) = xy + \frac{1}{x} + \frac{1}{y}$

It looks like you might need help with analyzing or working through these functions. Do you want to proceed with any specific task related to these functions, such as derivatives, integrals, or evaluating them? Feel free to let me know how you'd like to proceed!

Would you like me to:

1. Calculate partial derivatives for each function?
2. Simplify the expressions?
3. Perform a specific operation on these functions?
4. Analyze the behavior of these functions for given values of $x$ and $y$?
5. Provide any other mathematical insights?

Also, a quick tip: When dealing with multivariable functions, it’s always helpful to understand their partial derivatives to analyze their change with respect to each variable.