Definition:Derivative/Notation

Notation for Derivative

There are various notations available to be used for the derivative of a function $f$ with respect to the independent variable $x$:

$\dfrac {\d f} {\d x}$

$\map {\dfrac \d {\d x} } f$

$\dfrac {\d y} {\d x}$ when $y = \map f x$

$\map {f'} x$

$\map {D f} x$

$\map {D_x f} x$

When evaluated at the point $\tuple {x_0, y_0}$, the derivative of $f$ at the point $x_0$ can be variously denoted:

$\map {f'} {x_0}$

$\map {D f} {x_0}$

$\map {D_x f} {x_0}$

$\map {\dfrac {\d f} {\d x} } {x_0}$

$\valueat {\dfrac {\d f} {\d x} } {x \mathop = x_0}$

and so on.

Leibniz Notation

Leibniz's notation for the derivative of a function $y = \map f x$ with respect to the independent variable $x$ is:

$\dfrac {\d y} {\d x}$

Newton Notation

Newton's notation for the derivative of a function $y = \map f t$ with respect to the independent variable $t$ is:

$\map {\dot f} t$

or:

$\dot y$

which many consider to be less convenient than the Leibniz notation.

This notation is usually reserved for the case where the independent variable is time.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): prime: 5.
• 1990: H.A. Priestley: Introduction to Complex Analysis (revised ed.) ... (previous) ... (next): Notation and terminology