Partial derivative

what is a 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

Category: Bank

Similar articles: