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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 ...
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 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 .
Change in Tandem 2 1.2 Rates of Change 2 1.3 Rates of Change in Linear and Quadratic Functions 2 1.4 Polynomial Functions and Rates of Change 2 1.5 Polynomial Functions and Complex Zeros 2 1.6 Polynomial Functions and End Behavior 1 1.7 Rational Functions and End Behavior 2 1.8 Rational Functions and Zeros 1 1.9
In the context where it is defined, the derivative of a function is a measure of the rate of change of function values with respect to change in input values. Because a constant function does not change, its derivative is 0. [5] This is often written: () ′ =. The converse is also true.
This page was last edited on 22 February 2019, at 00:58 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
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Construct an equation relating the quantities whose rates of change are known to the quantity whose rate of change is to be found. Differentiate both sides of the equation with respect to time (or other rate of change). Often, the chain rule is employed at this step. Substitute the known rates of change and the known quantities into the equation.
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