What Do You Understand When You Say Derivative?

What is one of the most difficult topics in mathematics?

Derivative!

Yes, derivative is a very difficult subject in mathematics.

So what does derivative mean?

The literal meaning reminds me of something derived from something. A derivative of something, that is, something derived from something else.

For some reason, while translating the terms in mathematics into Turkish, Ataturk gave the name derivative to the operation formerly known as "mustak" in mathematics.

Isaac Newton discovered this process!

Although Leibniz also discovered the same process at that time, the fundamental book of mathematics that we call Calculus today is attributed to both of them.

I wrote about this topic before.

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Today, in mathematics, we use many terms that Atatürk coined during his time.

Look, I even used the term derivation in this sentence. The derivative must be strictly related to derivation.

I wonder why Ataturk called this process derivative?

After that, no one ever sat down and thought about mathematical terms again and did not come up with any new terms properly.

I think we should think a little about terms in mathematics.

Today we have to use many words that are not really Turkish.

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I'm looking at the TDK dictionary to see what a derivative is, and I'm getting confused.

TDK tried to explain derivative mathematics by saying "the limit of the ratio of the increase of the function to the increase of the variable as the increase of the variable goes to zero" and I think he made a confusing explanation.

According to Wikipedia, the derivative is defined as "Although it is generalized for functions on other number sets, it is primarily defined for real-valued functions of one variable, that is, from real numbers to real numbers. It is the tangent value of the positive angle made by any tangent to any curve with the x-axis." It was tried to be explained with a very long, technical and complex explanation.

The etymological dictionary has already stated that the etymology of the word comes from the verb "derive" and says look at the word derimak. The meaning of derivation is already clear. He didn't write anything about its mathematical equivalent.

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Does anyone know what this so-called derivative is?

What does it do?

Does it have any benefits in daily life?

I don't remember in which grade we learned it in high school, maybe it was senior year. We learned it in great detail in mathematics classes in our first year of university.

We use derivative operations for many formulas in civil engineering, especially in water mechanics courses. We use it in formulas in many places in courses of other branches.

There are many rules for the derivative operation in mathematics, and you have to memorize most of the rules to take the derivative of a function.

Actually, derivative is a limit operation, but many people do not know this limit operation.

Don't ask what the limit process is, it's a limit, it's like approaching the limits of something.

In schools, students mostly learn derivatives using ready-made memorized rules, and when the school years are over, the derivative rules memorized are forgotten.

The so-called derivative process is of no use to us in daily life anyway.

In fact, the process we call derivative is simply a process that helps us find the slope of a function at any point.

Since there is a term called "function" even in this simple definition, I now perceive this definition as a rather technical term.

To understand this definition, we must first understand what a function is.

What we call a function means a formula written depending on one or more variables, and if formulas and variables are involved, stop trying to solve it; neither the function nor the derivative seem like something that has any practical use.

Some people may say that I studied social sciences, but I am not good at mathematics.

Those who say so are right. Indeed, the derivative operation of mathematics has no place in social sciences.

Actually, the derivative has no practical use in our daily life.

But for some reason they teach it in math classes.

Occasionally, a few people will be interested in scientific subjects and will use derivatives and integrals in their professional lives.

Just for this reason, they keep giving so many young people trouble in schools.

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But look, if we are talking about life, there is such a thing as derivative transactions in the stock market.

There are also some investment products that banks offer as derivative products.

Those associated with money at least use this term in their daily speech. Even if they don't know its meaning, at least they know that there is such a thing as derivatives in the financial world.

Derivative products are “products whose value varies with changes in the value of an underlying asset. They are used to protect against risk or to increase returns by taking a certain level of risk. "The most typical features are that they have variability values due to time due to maturity and price fluctuations in the spot market," explained a source.

Look, when it comes to derivative products, we are talking about something variable. But this statement also talks about taking risks.

This means that derivative products are risky products. But if you're lucky, the returns can be high!

Can you create your own luck?

Maybe, if you are careful and invest in the right thing at the right time, if you can end that investment at the right time may happen.

Could derivatives in financial matters have anything to do with mathematics?

I don't think so; derivative transactions, or derivative products, are subjects that are in line with the direct meaning of the derivative.

I think the word derivative is used in its proper sense here.

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Let's go back to the derivative in mathematics.

In fact, when climbing a mountain, we can say that the derivative is the slope of the mountain at that location.

In a sense, we can call the speed of the vehicle we use a derivative.

When we look, the speed value we see on the speed dial of the vehicle is actually the derivative of the road with respect to time.

If we were able to write a mathematical function based on the travel time of the route we follow, the speed value at that moment when we look at the dial is equal to the derivative value of that travel-time function we wrote at that moment.

In other words, the derivative of the distance-time function is the speed function.

Look, derivatives actually have a place in daily life.

We just don't realize it.

At one point, I stepped on the gas so much that I saw that the speedometer was showing 160 km/h.

In other words, the highest slope of the road-time graph was 160 km/h at one point.

The current slope of the graph gives the maximum speed value.

See, it also means derivative slope.

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My goal is not to take you back to your high school years and confuse you again by delving into the complicated formulas of mathematics.

Actually, I started this article by wondering if we could find a more understandable term for the derivative operation used in mathematics.

Okay, it is a derivative Turkish word, our great leader thought of this term himself. In fact, it is a term that has been established in mathematics for all these years, and I have no objection to it.

However, it seems to me that the term derivative is not a term that fully suits its function and real meaning.

As I just wrote, when it comes to derivative products that are used exactly in line with their function in financial matters, I think they do not have the appropriate meaning in mathematics.

They have a hard time defining it even in the dictionary, and I think they haven't defined it correctly anyway.

It would be useful for someone to look at the definition in the dictionary once again. At least it is not an understandable definition, it should be corrected in a more understandable way.

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What do you think could be another word suitable for its meaning that can be used instead of derivative?

I just tried to explain its practical use in life.

It seems to me that derivative is a process related to change.

The rate of change in the values of a function!

Okay, after all, it is another function derived from a derivative function, but in principle, we obtain a new function related to the change of that function by doing the derivative operation.

Also, the integral is another function derived from a function, just like the derivative. What is the difference between derivative and integral then?

You know, when they say the inflation rate is decreasing, they are talking about the downward change in the inflation rate. So they're not actually saying that prices are falling.

The slope of the inflation curve has decreased a little, it has bent its neck a little bit, that's all! Although the derivative of the inflation curve does not give negative values, it has started to give slightly lower values than before.

If you believe, of course, believe in TURKSTAT data. I think those who say that we have broken the back of inflation are talking too much.

Prices are in a full-blown upward trend.

For example, what we call the derivative is the slope of the inflation curve. What they say is his back is broken, it's just a little less inclined.

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After all, the equivalent of the word derivative in European languages is derivation.

Although this word came to our language from French, it is essentially a word of Latin origin.

In construction, we call it a diversion tunnel. Before building a dam on a river, a tunnel is built inside the mountain and the bed of the river is changed and the river is directed to that tunnel. Thus, construction works can be started at the dam site of the river without any water problems.

The diversion tunnel serves to change the direction of water.

The Latin word derivation is derived from the word "rivus", river, (English river!). It means to change the direction of the river, to turn it in another direction. De-river.

We can say that the meaning of the word derivation, which is used instead of derivative in European languages, is somewhat related to the operation performed in mathematics, but I think they could not express its full meaning.

I think it can be called the change function instead of the derivative, because it is the process that gives the change function of the function, the derivative function gives its slope graphically. But first we need to find a Turkish equivalent for the function.

In social science, the word "function" is used instead of function.

I think this term can also be used in mathematics. It also means that it sits quite well. After all, what we call a function in mathematics is a process in which we can obtain a result by subjecting one or more variables to a function.

So, we can say “function” instead of “function” and “change function” instead of “derivative”.

But the word derivative has been well established in our language all this time, why should we change it?

Derivative is nice, but people don't understand what it is, and it seems like a very difficult thing. When we say derivative, it seems like a mysterious process.

I think derivative transactions would be more memorable if they had a name appropriate to their meaning.

“The exchange function of a function is is calculated!”

It wasn't that bad. There are many functions in the sentence, but if we think a little more, maybe we can find a better word instead of derivative.

For example, what if we say direct slope?

“Here's how to calculate the slope of a function!”

Does the function have a slope? I don't think it happened like that.

What if we just say change?

“The change of a function is calculated like this!”

I guess it happened.

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Look, the word "calculus" is stuck in my mind now, and "calculus" is not Turkish, it is an Arabic language.

What should we say instead of account?

Although there are accounting experts and so on, accounting is a word that is well established in our language.

Then there is the term accountability.

Being accountable is important!

I think it would be beneficial for someone to sit down and at least coin new terms in mathematics.

Ataturk initiated this change, but as always, we turned our backs after him.

There are so many math terms that need to be changed! Trigonometry terms, sine, cosine, tangent, rational numbers, complex numbers, series, integral... Even the word mathematics is Latin.

Many of us are not smart about mathematics anyway, and we learn mathematics with a lot of strange terms.

They still teach mathematics in schools, right?

Or did they think there was no need and gave up on math classes?

I can't follow the latest curriculum in schools anymore.

Believe me, I would not be surprised if they removed mathematics from the curriculum completely because it has no place in social sciences.

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Math is important.

Stay with math.

With love and respect to everyone from Moscow.