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.
 | This article uses too much jargon, which needs explaining or simplifying. (February 2024) |
For partial derivatives of function f with respect to variable x, the notation
, ,
is standard,[1][2][3] but other notations are sometimes used.
If we have a function , then there are several partial derivatives of f(x, y) that are all equally valid. For example,
![{\displaystyle {\frac {\partial }{\partial y}}[f(x,y)]=1}](http://wikimedia.org/api/rest_v1/media/math/render/svg/4f34b30b8bb979d462c1f83b3de536e27050b697)
Or, we can do the following:
![{\displaystyle {\frac {\partial }{\partial x}}[f(x,y)]=2x}](http://wikimedia.org/api/rest_v1/media/math/render/svg/cbe7e2f4c3a266a75c3219c4c76ab2ec4fb0799f)
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