Definition:Nth Derivative/Notation

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$n$th Derivative: Notation

The $n$th derivative of $\map f x$ can variously be denoted as:

$D^n \map f x$
$D_{\map x n} \map f x$
$\dfrac {\d^n} {\d x^n} \map f x$

The $n$ in $f^{\paren n}$ is sometimes written as a roman numeral, but this is considered on $\mathsf{Pr} \infty \mathsf{fWiki}$ as being ridiculously archaic.

If the $n$th derivative exists for a function, then $f$ is described as being $n$ times differentiable.


"... and so on."