Dot / time derivative (ẋ) in LaTeX
\dot{x} places a single dot over a symbol, Newton's notation for a first derivative with respect to time. \ddot{x} adds two dots for the second time derivative.
LaTeX command
\dot{x}Not the symbol you meant? Draw it to find the command →
\dot{x} is a math-mode accent used mainly in mechanics for a time derivative, so \dot{x} means dx/dt and \ddot{x} means d^2x/dt^2. Both need no package and render in KaTeX. The notation is compact for equations of motion, where writing dx/dt repeatedly would be cumbersome.
Use \dot for one dot, \ddot for two and \dddot for three (\dddot needs amsmath in full LaTeX and is also supported by KaTeX). Beyond three dots the notation becomes hard to read, so most authors switch to Leibniz form, d^n x / dt^n, or a parenthesised superscript such as x^{(4)}.
Do not confuse this accent with the operators \cdot (a centred multiplication dot) or \bullet. \dot is an accent sitting above a symbol, whereas \cdot is a binary operator, a dot centred at the height of a minus sign. Like \bar and \vec, the dot accent is sized for a single character.
Other forms
\ddot{x}second derivative (ẍ)Examples
$\dot{x} = \frac{dx}{dt}$velocity as a time derivative
$\ddot{x} = \frac{d^2x}{dt^2}$acceleration
$m\ddot{x} + c\dot{x} + kx = 0$a damped oscillator
$\dot{\theta}$an angular velocity
$L = \tfrac{1}{2}m\dot{q}^2 - V(q)$a Lagrangian in generalised coordinates
Tips and common mistakes
\dot{x}is the first time derivative and\ddot{x}the second; reserve dots for derivatives with respect to time to match convention.- For three dots use
\dddot{x}; beyond that switch to d^n/dt^n or x^{(n)} for readability. \dotis an accent (sits above the symbol);\cdotis a multiplication operator on the line. They are not interchangeable.- The dot accent fits one character, so apply it to a single letter such as
\dot{\theta}, not to a whole product. - Write
\dot{x}^2for (x-dot) squared;\dot{x^2}would dot the x-squared instead, which is different.
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Convert your maths to LaTeX →FAQ
What does \dot do in LaTeX?
puts one dot over the symbol, Newton's notation for a first derivative with respect to time (dx/dt).
How do I write two dots over a variable for acceleration?
Use , which renders two dots and denotes the second time derivative, d^2x/dt^2.
What is the difference between \dot and \cdot?
\dot{x} is an accent placed above a symbol for a derivative; \cdot is a centred dot used as a multiplication or dot-product operator, centred vertically on the line.