You seem to be listing several functions of two or three variables, possibly for analysis or differentiation purposes. These functions involve polynomials, exponentials, and other expressions. Let’s take a closer look at each one:

1. $f(x, y) = \frac{1}{3}x^3 - 3x^2 + \frac{y^2}{4} + xy + 13x - y + 2$
   This function contains cubic, quadratic, and mixed terms in $x$ and $y$, along with constants.

2. $f(x, y, z) = x^3 - 2x^2 + y^2 + z^2 - 2xy + xz - yz + 3z$
   A function involving three variables ($x, y, z$) with cubic and quadratic terms, as well as mixed terms like $xy$, $xz$, and $yz$.

3. $f(x, y) = x^3 + y^5 - 3x - 10y + 4$
   A function with higher-degree terms like $x^3$ and $y^5$, linear terms, and a constant.

4. $f(x, y) = \frac{1}{3}x^3 - x - \frac{1}{3}y^3 + y$
   A simpler function involving cubic and linear terms in both $x$ and $y$.

5. $f(x, y) = 2x^3 + 4y^2 - 2y^4 - 6x$
   A function that includes cubic, quadratic, quartic terms in $y$, and linear terms in $x$.

6. $f(x, y, z) = x^2 y - ye^z + 2x + z$
   This function contains a product of $x^2 y$, an exponential term $e^z$, and linear terms in $x$ and $z$.

7. $f(x, y) = -\frac{1}{2}xy + \frac{2}{x} - \frac{1}{y}$
   A rational function involving terms like $\frac{2}{x}$ and $\frac{1}{y}$, plus a mixed term in $xy$.

8. $f(x, y) = (x^2 - y^2)e^{-(x^2 + y^2)/2}$
   This function includes a quadratic term multiplied by an exponential decay factor involving both $x$ and $y$.

9. $f(x, y) = e^{-(x^2 + y^2)}(x^2 + 2y^2)$
   Similar to the previous function but with different factors in the polynomial and the exponential.

Would you like help with:

1. Finding the partial derivatives of these functions?
2. Analyzing the critical points or extrema?
3. Evaluating these functions for specific values of $x$, $y$, and $z$?
4. Finding gradient and Hessian matrices?
5. Plotting these functions for better visualization?

Tip: When working with multivariable functions, partial derivatives give insights into how the function behaves as each variable changes independently.