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Time derivative
From Wikipedia, the free encyclopedia
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as t.
A variety of notations are used to denote the time derivative. In addition to the normal notation,
two very common shorthand notations are also used: adding a dot over the variable, 
, 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
with the corresponding shorthands of 
and x''.
Time derivatives are a key concept in physics. For example, for a changing position x, its time derivative is its velocity, and its second derivative with respect to time, , is its acceleration. Even higher derivatives are sometimes also used: the third derivative of position with respect to time is known as the jerk.
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:
- force is the time derivative of momentum
- power is the time derivative of energy
- electrical current is the time derivative of electric charge
and so on.
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