Editing Multivariable calculus (section)

=== Partial derivative ===
{{Main article|Partial derivative}}
The partial derivative generalizes the notion of the derivative to higher dimensions.  A partial derivative of a multivariable function is a [[derivative]] with respect to one variable with all other variables held constant.<ref name="CourantJohn1999"/>{{rp|26ff}}

A partial derivative may be thought of as the directional derivative of the function along a coordinate axis.

Partial derivatives may be combined in interesting ways to create   more complicated expressions of the derivative.  In [[vector calculus]], the [[del]] operator (<math>\nabla</math>) is used to define the concepts of [[gradient]], [[divergence]], and [[Curl (mathematics)|curl]] in terms of partial derivatives.  A matrix of partial derivatives, the '''[[Jacobian matrix and determinant|Jacobian]]''' matrix, may be used to represent the derivative of a function between two spaces of arbitrary dimension.  The derivative can thus be understood as a [[linear transformation]] which directly varies from point to point in the domain of the function.

[[Differential equations]] containing partial derivatives are called [[partial differential equations]] or PDEs.  These equations are generally more difficult to solve than [[ordinary differential equations]], which contain derivatives with respect to only one variable.<ref name="CourantJohn1999"/>{{rp|654ff}}