Mixed partial derivative
= Mixed partial derivative
{title2=$f_{xy}$}
A mixed partial derivative takes <partial derivatives> in different variables, for example $f_{xy}=\partial_y(\partial_x f)$. If both second <partial derivatives> are continuous in a neighbourhood, their order can be interchanged: $f_{xy}=f_{yx}$. The <chain rule> transforms mixed partial derivatives under a linear <change of variables> by composing the corresponding first-order differential operators.