Partial derivative

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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

${\displaystyle {\frac {\partial f}{\partial x}}}$, ${\displaystyle f_{x}}$, ${\displaystyle \partial _{x}f}$

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

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.