MathLiveSymmetry of second derivatives
States that mixed second-order partial derivatives of a function are equal regardless of the order in which the differentiations are taken, provided the function and its relevant partial derivatives are continuous. It is used to swap the order of differentiation when computing or simplifying partial derivatives.
\frac{\partial^2 f}{\partial x\,\partial y} = \frac{\partial^2 f}{\partial y\,\partial x}What the symbols mean
| a real-valued function of two variables with continuous second partial derivatives | |
| the independent variables of f |
About this formula
- FieldMathematics
- TopicMultivariable calculus
- LevelUniversity
- Also calledClairaut's theorem, Schwarz's theorem, Young's theorem, mixed partial derivatives equality, equality of mixed partials, order of partial differentiation
- SourceWikidata Q1503239
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