Derivatives
"Now that you are familiar with limits, the door to calculus stands open. The first task is to introduce the fundamental concept of the derivative. Suppose a function ƒ represents a quantity of interest—for example, the variable cost of manufacturing an item, the population of a country, or the position of an orbiting satellite. The derivative of ƒ is another function, denoted ƒ′, that gives the slope of the curve y =ƒ(x) as it changes with respect to x. Equivalently, the derivative of ƒ gives the instantaneous rate of change of ƒ with respect to the independent variable. We use limits not only to define the derivative but also to develop efficient rules for finding derivatives. The applications of the derivative—which we introduce along the way—are endless because almost
everything around us is in a state of change, and derivatives describe change." (Briggs et al., 2019)
We will look at how to calculate derivatives later. For now, go the Integrals page, and let's look at how to calculate the volumes of solids.
"Now that you are familiar with limits, the door to calculus stands open. The first task is to introduce the fundamental concept of the derivative. Suppose a function ƒ represents a quantity of interest—for example, the variable cost of manufacturing an item, the population of a country, or the position of an orbiting satellite. The derivative of ƒ is another function, denoted ƒ′, that gives the slope of the curve y =ƒ(x) as it changes with respect to x. Equivalently, the derivative of ƒ gives the instantaneous rate of change of ƒ with respect to the independent variable. We use limits not only to define the derivative but also to develop efficient rules for finding derivatives. The applications of the derivative—which we introduce along the way—are endless because almost
everything around us is in a state of change, and derivatives describe change." (Briggs et al., 2019)
We will look at how to calculate derivatives later. For now, go the Integrals page, and let's look at how to calculate the volumes of solids.
If you have questions, please email me at [email protected]
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This website was prepared by Brant Breeding in his personal capacity. These materials are not endorsed, approved, sponsored, or provided by or on behalf of the University of Arkansas, Fayetteville.
Please follow this link for our full disclaimer statement.