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  2. Time derivative - Wikipedia

    en.wikipedia.org/wiki/Time_derivative

    The flow of net fixed investment is the time derivative of the capital stock. The flow of inventory investment is the time derivative of the stock of inventories. The growth rate of the money supply is the time derivative of the money supply divided by the money supply itself. Sometimes the time derivative of a flow variable can appear in a model:

  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. Related rates - Wikipedia

    en.wikipedia.org/wiki/Related_rates

    Differentiation with respect to time or one of the other variables requires application of the chain rule, [1] since most problems involve several variables. Fundamentally, if a function F {\displaystyle F} is defined such that F = f ( x ) {\displaystyle F=f(x)} , then the derivative of the function F {\displaystyle F} can be taken with respect ...

  5. 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.

  6. 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.

  7. 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 f {\displaystyle f} 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 f {\displaystyle f} is how the position is changing in time, that ...

  8. Total derivative - Wikipedia

    en.wikipedia.org/wiki/Total_derivative

    The rate of change of f with respect to x is usually the partial derivative of f with respect to x; in this case, ∂ f ∂ x = y . {\displaystyle {\frac {\partial f}{\partial x}}=y.} However, if y depends on x , the partial derivative does not give the true rate of change of f as x changes because the partial derivative assumes that y is fixed.

  9. Numerical differentiation - Wikipedia

    en.wikipedia.org/wiki/Numerical_differentiation

    This formula can be obtained by Taylor series expansion: (+) = + ′ ()! ″ ()! () +. The complex-step derivative formula is only valid for calculating first-order derivatives. A generalization of the above for calculating derivatives of any order employs multicomplex numbers , resulting in multicomplex derivatives.

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