Definition:Derivative/Higher Derivatives/Second Derivative/Notation

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Definition

The second derivative is variously denoted as:

$\map {f''} \xi$
$D^2 \map f \xi$
$D_{xx} \map f \xi$
$\map {\dfrac {\d^2} {\d x^2} } \xi$


If $y = \map f x$, then it can also expressed as $y''$:

$y'' := \map {\dfrac \d {\d x} } {\dfrac {\d y} {\d x} }$

and written:

$\dfrac {\d^2 y} {\d x^2}$


Leibniz Notation

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

$\dfrac {\d^2 y} {\d x^2}$


Newton Notation

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

$\map {\ddot f} t$

or:

$\ddot y$


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


Also see


Sources