Partial derivative: Difference between revisions

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In [[mathematics]], a '''partial derivative''' of a [[Mathematical function|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]].
In [[mathematics]], a '''partial derivative''' of a [[Mathematical function|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 <math>f(x_1,\dots,x_n)</math> is called a function of multiple variables if <math>n>1</math>. The partial derivative of <math>f</math> in the direction <math>x_i</math> at the point <math>(t_1,\dots,t_n)</math> is defined as
: <math>\frac{\part f}{\part x_i}(t_1,\dots,t_n)=\lim_{h\rightarrow 0}\frac{f(t_1,\dots,t_i+h,\dots,t_n)-f(t_1,\dots,t_n)}{h}
</math>


== Notation ==
== Notation ==
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== See also ==
== See also ==
*[[Total derivative]]
*[[Derivative]]
*[[Total derivative]][[Category:Suggestion Bot Tag]]

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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 xi is written as fxi or ∂f/∂xi. The partial derivative symbol is distinguished from the straight d that denotes the total derivative.

See also