What Are Some Common Real-life Applications of Derivatives?—Uses and Examples

What Are Derivatives?

In math, derivatives are known to express the rate at which a quantity changes based on a secondary quantity. It is among the most crucial concepts and has found extensive usage across different mathematical scenarios over the years. ¹

As is evident, derivatives are usually used when: 

(i) Either the quantity being studied is variable,

(ii) The rate of change is variable, or when

(iii) You want to study the relationship between a dependent variable and an independent variable. ²

Thus, derivatives are useful in many fields, including not only math but also physics and engineering.

In this article, we’ll explore some common real-life applications of derivatives. 

Let’s get started.

1. In the Automobile Industry

First on this list, we’ll discuss how the automobile industry uses derivatives in cars and vehicles. 

An automobile usually comes with both an odometer and a speedometer. These gauges are known to help the driver determine the speed at which they’re traveling. 

In addition to this, they can also find out the distance they’ve traveled so far. 

The electronic versions of these gauges often employ the use of derivatives to convert data from the tires into miles per hour, alongside the distance sent to the motherboard into kilometers.

2. In the Police Force

You might have seen police officers measure a car’s speed in several movies previously. But have you ever wondered how these guns employ the use of derivatives in real life? 

It’s very simple. Police officers using radar guns often utilize the power of derivatives to take aim and detect whether a driver is speeding. Whenever it is aimed at a vehicle, the radar gun can easily estimate the time and distance with which the radar hits some part of the vehicle. 

3. In Data Analysis 

A rather common application of derivatives in real life is centered around the use of graphs. Statisticians (and even others) often use derivative formulas to study graphs before calculating the gradient at any given point on the graph. 

You can use this method to analyze data collected from a survey or research, utilizing them across different use cases. 

4. In Physics 

The derivative of displacement of a body in motion (concerning time) is called its “velocity,” while the derivative of velocity concerning time is called its “acceleration.”

In addition, Newton’s second law of motion also states that the force acting on a body will determine its derivative momentum. ²

5. In Business

You might be surprised to know about the application of derivatives in business. Derivatives are employed every day in business in multiple ways. 

You must have seen graphs of business growth, expenses, profits, etc. in many presentations. 

These graphs derive their value from the input data punched in by the business.

Derivatives help in estimating the profit or loss of a business.  

6. In Seismology 

You may be aware of the magnitude of an earthquake, but have you ever wondered how it is measured? This can be measured easily, thanks to derivatives. 

In seismology, derivatives make it possible for scientists to determine the range of magnitude of an earthquake.

7. In Biology 

Using the concept of derivatives, scientists can forecast the growth rate of a virus. It helps them to study whether or not the virus is developing swiftly and whether or not countermeasures should be made to stop the expansion. 

Concepts related to derivatives were also used to study the growth rate of COVID-19 and its variants. 
8. In Chemistry 

The concept of derivatives finds extensive usage across different aspects of chemistry. 

Unlike math, derivatives are chemical compounds derived from other compounds (also known as a “parent compound”). This process usually involves using reagents, reactants, enzymes, and catalysts, among others. 

Chemical derivatives can be both simple and complex. They are commonly studied as part of organic chemistry. 

9. In Economics 

Decisions relating to economics involve critical analysis. Making decisions about potential investment gains and losses involves applying numerous statistical and mathematical techniques. 

With the use of derivatives, one can forecast the viability of an investment when the statistical data is reliant on numerous variables. 

By analyzing the result of derivatives, one can choose the best investment alternative. 

Derivatives are a crucial concept that is extremely useful in many real-life situations, whether it may be driving a car or making investment decisions. 

If you found this article useful and are fascinated by the world of math, visit BYJU’s FutureSchool blog, and read some more amazing content on math-related topics. 

References
Crisitina, S. (2021, July 16). Applications of Derivatives. Machine Learning Mastery. Retrieved October 29, 2022, from https://machinelearningmastery.com/applications-of-derivatives/
Johnson, J. (n.d.). Derivatives and their real world applications. Retrieved October 29, 2022, from https://thriveglobal.com/stories/derivatives-and-their-real-world-applications/