\begin{definition}[Definition:Derivative/Higher Derivatives/Higher Order]
The $n$th derivative of a function $y = \map f x$ is defined as:
:$\map {f^{\paren n} } x = \dfrac {\d^n y} {\d x^n} := \begin {cases}
\map {\dfrac \d {\d x} } {\dfrac {\d^{n - 1} y} {\d x^{n - 1} } } & : n > 0 \\
y & : n = 0 \end {cases}$
assuming appropriate differentiability for a given $f^{\paren {n - 1} }$.
\end{definition}