Symmetry of second derivatives
Teorema de Clairaut
- Date
- 1740-1909 · confidence low
- Place
- Paris, France
- Credited to
- Alexis Claude Clairaut, Hermann Schwarz y William Henry Young
- Field
- Knowledge & symbols
What was discovered
States that, under continuity conditions, the order in which partial derivatives of a multivariable function are taken does not change the result, i.e. mixed partial derivatives are equal.
What it led to
- Simplification of multivariable calculus in physics and engineering
- Criterion used to check whether a vector field is conservative
- Rigorous proof by Schwarz (1873) and relaxation of the hypotheses by Young (1909)