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# Partial Derivatives of Multivariable Functions in LaTeX

In mathematics, partial derivatives are used to study how a function of multiple variables changes with respect to a specific variable while keeping the other variables constant. In LaTeX, you can represent partial derivatives using the \partial command.

## Partial Derivatives of Multivariable Functions in LaTeX

In mathematics, partial derivatives are used to study how a function of multiple variables changes with respect to a specific variable while keeping the other variables constant. In LaTeX, you can represent partial derivatives using the \partial command.

## Using the \partial command

To write a partial derivative in LaTeX, use the \partial command combined with the symbols of the function and the variable. For example:


$$\frac{\partial f}{\partial x}$$


$$\frac{\partial f}{\partial x}$$

This represents the partial derivative of the function $f$ with respect to the variable $x$.

## Examples

Here are some examples of using the \partial command to represent partial derivatives in LaTeX:

1. Partial derivative of a function of two variables:


$$\frac{\partial^2 f}{\partial x \partial y}$$


$$\frac{\partial^2 f}{\partial x \partial y}$$

This represents the second mixed partial derivative of the function $f$ with respect to $x$ and $y$.

2. Higher-order partial derivatives:


$$\frac{\partial^3 f}{\partial x^2 \partial y}$$


$$\frac{\partial^3 f}{\partial x^2 \partial y}$$

This represents the third-order partial derivative of the function $f$: two derivatives with respect to $x$ and one derivative with respect to $y$.

These examples show how to use the \partial command to represent partial derivatives of multivariable functions in LaTeX.