Newton's notation

Newton's notation for differentiation, or dot notation, uses a dot placed over a function name to denote the time derivative of that function. Newton referred to this as a fluxion. (See Article 567 of Florian Cajori's book on A History of Mathematical Notations.[1])

Isaac Newton's notation is mainly used in mechanics. It is defined as:

$\dot{x} = \frac{dx}{dt} = x'(t)$
$\ddot{x} = \frac{d^2x}{dt^2} = x''(t)$

and so on.

Dot notation is not very useful for higher-order derivatives, but in mechanics and other engineering fields, the use of higher than second-order derivatives is limited.

Newton did not develop a standard mathematical notation for integration but used many different notations; however, the widely adopted notation is Leibniz's notation for integration.

In physics, macroeconomics and other fields, Newton's notation is used mostly for time derivatives, as opposed to slope or position derivatives.