In mathematical analysis, Clairaut's theorem states that if Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of figures and numbers. Mathematical knowledge is constantly growing, through research and application, but mathematics itself is not usually considered a natural science. ... Analysis is that branch of mathematics which deals with the real numbers, complex numbers, and their functions. ...

has continuous second partial derivatives at then for In mathematics, a continuous function is one in which arbitrarily small changes in the input produce arbitrarily small changes in the output. ... In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables with the others held constant. ...

In words, the partial derivatives of this function commute. This theorem is named for the French mathematician Alexis Clairaut. Alexis Claude Clairault (or Clairaut) ( May 3, 1713 - May 17, 1765) was a French mathematician. ...

See also

• Symmetry of second derivatives