One of the most useful applications of differentiation is found in the problems involving the rate of change of one quantity w.r.t another. For a long time, mathematicians struggled with the development of a method to find the related relation between the rate of change of quantities like the perimeters, areas or volumes of a two dimensional or three dimensional figures when one or more of the variables defining the figure kept changing. It was then, that the theory of related rates was developed with the help of derivatives.

We have always been interested in a wide variety of time rates: the rate at which the speed of a vehicle is increasing, the rate at which the amount of ...

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