# Partial derivative

From Citizendium, the Citizens' Compendium

In mathematics, a **partial derivative** of a function of several variables is its derivative with respect to one of those variables while all others are kept constant. Partial derivatives are widely used in differential geometry, vector calculus, and physics.

## Definition

A function is called a function of multiple variables if . The partial derivative of in the direction at the point is defined as

## Notation

The partial derivative of a function *f* with respect to the variable *x _{i}* is written as

*f*

_{xi}or

*∂f/∂x*. The partial derivative symbol

_{i}*∂*is distinguished from the straight

*d*that denotes the total derivative.