\begin{definition}[Definition:Partial Derivative/Higher Derivative/Fourth Derivative]
Let $u = \map f {x, y, z}$ be a function of the $3$ independent variables $x$, $y$ and $z$.
The following is an example of one of the $4$th derivatives of $f$:
:$\dfrac {\partial^4 u} { \partial x \partial y \partial z^2} := \map {\dfrac \partial {\partial x} } {\dfrac {\partial^3 u} {\partial y \partial z^2} } =: \map {f_{3 3 2 1} } {x, y, z}$
\end{definition}