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Partial Derivatives of Multivariable Functions in LaTeX

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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.