Search results
Results from the WOW.Com Content Network
[5] [6] The difference quotient is a measure of the average rate of change of the function over an interval (in this case, an interval of length h). [7] [8]: 237 [9] The limit of the difference quotient (i.e., the derivative) is thus the instantaneous rate of change. [9]
In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...
For this reason, the derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. [1] The process of finding a derivative is called differentiation .
Informally, the second derivative can be phrased as "the rate of change of the rate of change"; for example, the second derivative of the position of an object with respect to time is the instantaneous acceleration of the object, or the rate at which the velocity of the object is changing with respect to
Rate of change may refer to: Rate of change (mathematics) , either average rate of change or instantaneous rate of change Instantaneous rate of change , rate of change at a given instant in time
For any fixed b not equal to 1 (e.g. e or 2), the growth rate is given by the non-zero time τ. For any non-zero time τ the growth rate is given by the dimensionless positive number b. Thus the law of exponential growth can be written in different but mathematically equivalent forms, by using a different base.
In multivariable calculus, the directional derivative measures the rate at which a function changes in a particular direction at a given point. [citation needed]The directional derivative of a multivariable differentiable (scalar) function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a direction ...
The instantaneous phase (also known as local phase or simply phase) of a complex-valued function s(t), is the real-valued function: = {()}, where arg is the complex argument function. The instantaneous frequency is the temporal rate of change of the instantaneous phase.