Definition:Derivative/Notation

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Notation for Derivative

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

  • $\dfrac {\d f} {\d x}$
  • $\dfrac \d {\d x} \left({f}\right)$
  • $\dfrac {\d y} {\d x}$ when $y = f \left({x}\right)$
  • $f' \left({x}\right)$
  • $D f \left({x}\right)$
  • $D_x f \left({x}\right)$


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

  • $f' \left({x_0}\right)$
  • $D f \left({x_0}\right)$
  • $D_x f \left({x_0}\right)$
  • $\dfrac {\d f} {\d x} \left({x_0}\right)$

and so on.


Leibniz Notation

Leibniz's notation for the derivative of a function $y = f \left({x}\right)$ with respect to the independent variable $x$ is:

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


Newton Notation

Newton's notation for the derivative of a function $y = f \left({t}\right)$ with respect to the independent variable $t$ is:

$\dot f \left({t}\right)$

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.