what is a derivative?

In mathematics, the derivative is
a way to show rate of change: that is, the amount by which a function is changing at one given point. For functions that act on the real numbers, it is the slope of the tangent line at a point on a graph. The derivative is often written using "dy over dx" (meaning the difference in y divided by the difference in x). The d is not a variable, and therefore cannot be cancelled out.

Some real life applications of derivatives are:

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automobiles

In an automobile there is always an odometer and a speedometer. These two gauges work in tandem and allow the driver to determine his speed and his distance that he has traveled. Electronic versions of these gauges simply use derivatives to transform the data sent to the electronic motherboard from the tires to miles per Hour(MPH) and distance(KM).

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radar guns

Police officers who use radar guns are actually taking advantage of the easy use of derivatives. When a radar gun is pointed and fired at your care on the highway. The gun is able to determine the time and distance at which the radar was able to hit a certain section of your vehicle. With the use of derivative it is able to calculate the speed at which the car was going and also report the distance that the car was from the radar gun.

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business

In the business world there are many applications for derivatives. One of the most important application is when the data has been charted on graph or data table such as excel. Once it has been input, the data can be graphed and with the applications of derivatives you can estimate the profit and loss point for certain ventures.

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graphs

The most common application of derivative is to analyze graphs of data that can be calculated from many different fields. Using derivative one is able to calculate the gradient at any point of a graph.

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climate change

In measuring how quickly the temperature is changing or icecaps are melting, scientists can determine the severity of various situations through the use of derivatives.

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optimization

This can be especially useful in the world of economics. Because derivatives can be used to find the maximum and minimum values of a function with ease, if we are given a trend and can find a curve of best fit, we can use the derivative of that curve to find high and low points.

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thank you for reading!!

made by Afifa Monzur 10F