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### Partial derivative

The **partial derivative** of a function *f* of a number of variables, is the derivative in which just one of the variables is treated and the others as constants

in which the symbol ∂ is used.

##### Explanation

Other notations are

These different notations are often used interchangeably. That seems confusing, but in practice it is quite usefull.

##### Example 1

The most general form of the Schrödinger equation is

where is the differential operator.

##### Example 2

The laplacian of a function *f* in ℝ^{n} coordinates is

where is the differential operator.

## HistoryThe French mathematician Adrien-Marie Legendre (1752 - 1833) introduced the symbol ∂ for the partial derivative. The German mathematician Carl Jacobi (1804 - 1851) later used it again. |