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Partial derivative

From Simple English Wikipedia, the free encyclopedia

In multivariable calculus, the partial derivative of a function is the derivative of one variable when all other variables are held constant. In other words, a partial derivative takes the derivative of certain variables of a function while not differentiating other variable(s). Partial derivatives are often used in multivariable functions.

For partial derivatives of function f with respect to variable x, the notation

, ,

is standard,[1][2][3] but other notations are sometimes used.


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If we have a function , then there are several partial derivatives of f(x, y) that are all equally valid. For example,

Or, we can do the following:

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  1. "List of Calculus and Analysis Symbols". Math Vault. 2020-05-11. Retrieved 2020-09-16.
  2. Weisstein, Eric W. "Partial Derivative". mathworld.wolfram.com. Retrieved 2020-09-16.
  3. "Calculus III - Partial Derivatives". tutorial.math.lamar.edu. Retrieved 2020-09-16.