# Partial derivative

This article describes an analogue for functions of multiple variables of the following term/fact/notion for functions of one variable: derivative

## Definition at a point

### Generic definition

Suppose is a function of more than one variable, where

is one of the input variables to . Fix a choice and fix the values of all the other variables. The**partial derivative**of with respect to

*at the point*. denoted , or

src="/img/110/698a83383e6178667d47be974006dabb253.png" />

, is defined as the derivative at of the function that sends to at for the same fixed choice of the other input variables.### For a function of two variables

Directional derivative at

with respect to a unit vector in the positive -direction.Directional derivative at

with respect to a unit vector in the positive -direction.### For a function of multiple variables

Source: calculus.subwiki.org

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