Definition:Nth Derivative/Notation

$n$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 this website as being ridiculously archaic.

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

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 13$: Higher Derivatives: $13.45$
• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 10.2$

"... and so on."

• 1990: H.A. Priestley: Introduction to Complex Analysis (revised ed.) ... (previous) ... (next): Notation and terminology
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): derivative
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): derivative
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): order: 1. (of a derivative)