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Time Derivative




A variety of notations are used to denote the time derivative. In addition to the normal notation,

: rac {dx} {dt}

two very common shorthand notations are also used: adding a dot over the variable, \dot{x}, and adding a Prime to the variable, x'. These two shorthands are generally not mixed in the same set of equations.

Higher time derivatives are also used: the Second Derivative with respect to time is written as

: rac {d^2x} {dt^2}

with the corresponding shorthands of \ddot{x} and x''.

Time derivatives are a key concept in .

A large number of fundamental equations in physics involve first or second time derivatives of quantities. Many other fundamental quantities in science are time derivatives of one another:



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