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  2. Time derivative - Wikipedia

    en.wikipedia.org/wiki/Time_derivative

    The growth rate of output is the time derivative of the flow of output divided by output itself. The growth rate of the labor force is the time derivative of the labor force divided by the labor force itself. And sometimes there appears a time derivative of a variable which, unlike the examples above, is not measured in units of currency:

  3. Fourth, fifth, and sixth derivatives of position - Wikipedia

    en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth...

    Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.

  4. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    The higher order derivatives can be applied in physics; for example, while the first derivative of the position of a moving object with respect to time is the object's velocity, how the position changes as time advances, the second derivative is the object's acceleration, how the velocity changes as time advances.

  5. Differential calculus - Wikipedia

    en.wikipedia.org/wiki/Differential_calculus

    This states that differentiation is the reverse process to integration. Differentiation has applications in nearly all quantitative disciplines. In physics, the derivative of the displacement of a moving body with respect to time is the velocity of the body, and the derivative of the velocity with respect to time is acceleration.

  6. Time-scale calculus - Wikipedia

    en.wikipedia.org/wiki/Time-scale_calculus

    The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale (also known as a time-set), which may be an arbitrary closed subset of the reals. In this way, results apply not only to the set of real numbers or set of integers but to more general time scales such as a Cantor set.

  7. Related rates - Wikipedia

    en.wikipedia.org/wiki/Related_rates

    The rate of change is usually with respect to time. Because science and engineering often relate quantities to each other, the methods of related rates have broad applications in these fields. Differentiation with respect to time or one of the other variables requires application of the chain rule, [1] since most problems involve several variables.

  8. Discrete calculus - Wikipedia

    en.wikipedia.org/wiki/Discrete_calculus

    If the input of the function represents time, then the difference quotient represents change with respect to time. For example, if is a function that takes a time as input and gives the position of a ball at that time as output, then the difference quotient of is how the position is changing in time, that is, it is the velocity of the ball.

  9. Generalizations of the derivative - Wikipedia

    en.wikipedia.org/wiki/Generalizations_of_the...

    The convective derivative takes into account changes due to time dependence and motion through space along a vector field, and is a special case of the total derivative. For vector-valued functions from R to R n (i.e., parametric curves ), the Fréchet derivative corresponds to taking the derivative of each component separately.