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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. [1] The variable denoting time is usually written as t {\displaystyle t} .
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 = = =.
The delta integral is defined as the antiderivative with respect to the delta derivative. ... for functions on time scales, which uses the same table of transforms ...
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. Derivatives can be generalized ...
The last expression is the second derivative of position (x) with respect to time. On the graph of a function, the second derivative corresponds to the curvature or concavity of the graph. The graph of a function with a positive second derivative is upwardly concave, while the graph of a function with a negative second derivative curves in the ...
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 ...
velocity is the derivative (with respect to time) of an object's displacement (distance from the original position) acceleration is the derivative (with respect to time) of an object's velocity, that is, the second derivative (with respect to time) of an object's position. For example, if an object's position on a line is given by
In calculus, the differential represents the principal part of the change in a function = with respect to changes in the independent variable. The differential is defined by = ′ (), where ′ is the derivative of f with respect to , and is an additional real variable (so that is a function of and ).