Hi everyone! Sure that everyone who went through high school or baccalaureate. .
. . .
. had suffered this about derivatives But what are the derivates? What are they for?
Intro What are the derivatives for? The derivatives, have to do with the functions . .
. . .
. so let's talk about the functions, through a simple example. FUNCTIONS What is a function?
So, a function is the relation between the input data and the output data. Although now it does not seem like that, they serve for many things They can represent lots of processes, situations, data . .
. . .
. For example. .
. Imagine that I'm going from my house to my girlfriend's house, which happens to be the "Khaleesi" . .
. ["Ecchi music"] Well, so it takes me 30 minutes to get to Vaes Dothrak, the capital of the Dothraki. .
. Where lives my Khaleesi. .
. Could I use a function to describe how much space I had traveled at each moment of that half hour? Of course!
. . .
The entry data is time; and, the output data, the space traveled. If I go all the time at the same speed, the function will look like this . .
. And if happens that I have found a nice horse, and I go faster but with a constant speed . .
. It will look like this, isn't it? .
. . Look at that!
. . .
To travel the same space, I have taken less time. And the function has a higher slope, that is, that between more speed, more inclined; and at a lower speed, less inclined. But.
. . And, if I have been changing speed .
. . How will the graphics be?
Ok. . .
Let's watch these spoles. . .
I was distracted, looking at the cell phone. Then the matter could be seen like this. We would have a graph with variations of inclination.
Ok, so, the derivative is that one which will help us to measure at each point how fast I was going. DERIVATIVES Imagine, I want to know what speed I was at minute 15 exactly. I can measure the space I traveled between minute zero until the 30th minute, and make the arithmetic mean.
Although it is a very ugly approach. . .
But instead of taking the 30 minutes, I could take 5 minutes, one minute, one second, one tenth, one thousandth. With a derivative you can measure the limit of the change when the time interval tends to zero . .
. . .
. I mean, the function measures the space that I have traveled and the time that has passed. .
. . .
. And what the derivative is measuring is THE SPEED in each point. .
. What happens is that when the function has a formula the derivative can be obtained. .
. Through a mathematical operation (by means of that formula) There are simpler formulas, which are those that are studied in high school. .
. . .
. Although those who study them think that there is nothing more difficult in the world. And there are other more complicated ones.
So, if you want to be engineer, mathematician, physicist, economist . . .
You will use derivatives, and it is best that you understand them. And if you do not. .
. ¡All the Khaleesi fury will fall on your heads! Until the next video.
