Why in the World we Need Derivatives Many years ago humans discovered that with the use of mathematical calculations many things can be calculated in the world and even the universe. Mathematics consists of many different operations. The most important that is used by mathematicians, scientists and engineers is the derivative. Derivatives can help make calculations of anything with respect to another event or thing. Derivatives are mostly common when used with respect to time. This is a very important tool in this revolutionary world.
With derivatives we can calculate the rate of change of anything with respect to time. This way we can have a sort of knowledge of upcoming events, and the different behaviors events can present. For example the population growth can be estimated applying derivatives. Not only population growth, but for example when dealing with plagues there can be certain control. An other example can be with diseases, taking all this events together a conclusion can be made.
The population of the world is growing extremely fast. Eventually there is going to be overpopulation and resources are going to run out if something is not done. We know earth is overpopulated and that a control over population can be made or at least something can be done so there is not a catastrophe. Population growth can be determined using exponential's which directly relate to derivatives. This is a tool that can be very helpful for anthropologist and sociologists in the world (which have nothing to do with mathematics). Not only to know population numbers in ten or twenty years but to have control over other things.
For example will there be enough food for five billion people in the world, will there be enough mineral supply for five billion people in the world or will there be enough fuel supply for five billion people in the world. Many of those types of investigations can be determined with the application of derivatives. The world population is growing extremely fast, and our natural resources are been consumed even faster, this study using exponential's and its graphs gives us an idea of what must be done to prevent a disaster. Around this fact of overpopulation and running out of natural resources many things have been created. Indirectly derivatives have caused all this and in some way it is very useful and important. For example birth control methods are a consequence of this.
Also there is something which is called the green revolution, this is something created to produce crops faster. Better fertilizers and pest controls have been created so crops can grow faster and in more quantity. This has been created by the fact the demand for food is growing more and more everyday. Also electrical cars which give a better mileage per gallon have been developed, this can help our fuel supply last longer and do not pollute so much helping the earth last a little bit longer. Many other important developments have been done so our planet earth can at least last for some couple hundred years more. Knowing the rate at which the population is growing is also very useful to make cities and countries better.
For example if the population of certain city is estimated to be five million in 10 years then the government entities will know how many more universities, schools, hospitals, police departments, banks etc, etc etc... There are hundreds of factors that should be considered as population increases. Derivatives have many application in many different areas. When dealing with volumes this is very important. For example a pool, need chloride but there is an exact measure that should be added. Or for example in factories that deal with containers of solutions that need to be mixed with other chemicals and then packaged, when gasoline is made, detergents, fertilizers etc, etc, etc...
We have an equation that is dQ / dt = rate in- rate out. Q is the amount of substance that is been mixed. Exponential growth plays a very important role in business. With this a control on economy growth can be maintained. This permits economists and governments can control their economy and see what affected the economy and how can it be better. Interest rates can be calculated with the rate of change.
With this we can calculate the growth of bank accounts. Also for example when buying a house we can choose what will be the best for our needs. Or when buying a car what will be the payment method. A simple formula can be applied to make all this calculations: T' = rT +- K (r is interest rate, K is money in or money out). When depositing money in an account you get the following formula T = ce^ (rt) - K / r. With this the account balance can be calculated, even on long term.
With these calculations people can control there money better, and know how much they can expend without spending it all stupidly. Finally to mention the most known application of derivative is when dealing with velocity. To calculate velocity we take the position function and differentiate it, and when differentiating again acceleration is obtained. This is of no use for the driver or the owner of the car; this is useful for us engineers when constructing a car. With these we can find out how fast will the car, that we built, go. All this is kinematics which is solved using derivatives.
Derivatives are in fact one of the most important tools mathematics has. Many things can be calculated with the application of them. Not only in the completion of our studies but when dealing with the real world. Probably we do not use them indirectly, but they are indeed present in our everyday lifes. As previously mentioned when we open bank accounts, when we see how much gas our car is spending per mile, when we have a credit card etc, etc, etc... There thousands of events that involved derivatives one way or the other.