# Symmetry of second derivatives

In mathematics, the **symmetry of second derivatives** (also called the **equality of mixed partials**) refers to the possibility of interchanging the order of taking partial derivatives of a function

of *n* variables without changing the result under certain conditions (see below). The symmetry is the assertion that the second-order partial derivatives satisfy the identity

so that they form an *n* × *n* symmetric matrix, known as the function's Hessian matrix. Sufficient conditions for the above symmetry to hold are established by a result known as **Schwarz's theorem**, **Clairaut's theorem**, or **Young's theorem**.[1][2]

In the context of partial differential equations it is called the **Schwarz integrability condition**.