Lesson 1 - What Is A Derivative? (Calculus 1 Tutor)
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- เผยแพร่เมื่อ 15 ก.ค. 2024
- This is just a few minutes of a complete course.
Get full lessons & more subjects at: www.MathTutorDVD.com.
In this lesson we discuss the concept of the derivative in calculus. First, we will discuss what is a derivative in simple terms and work numerous derivative examples. Next we will explain how derivatives work in calculus including the rules of derivatives.
![The Derivative in Calculus Defined as a Limit - [1-2]](http://i.ytimg.com/vi/9boavjdulxY/mqdefault.jpg)
![The Derivative in Calculus Defined as a Limit - [1-2]](/img/tr.png)
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Excellent. This concept could not have been explained any simpler. This teacher should teach the teachers how to teach calculus.......
He's an awesome teacher because he knows the material like the back of his hand and he has excellent communication skills. He's concise, precise and to the point. Most teachers and professors don't have the second quality. I'll mention two more that Jason has: one is patience and the other a genuine desire to help people understand this material. This comes across right away. In short, he's a God-send. Thank you, teacher Jason.
why isnt this not taught in scools,removes the ambiguity,step by step,language has a lot to answer for,we can all be smart with teaching of this magnitude.thank you.there are not many like you.
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@@user-ki6pt2zg1h aa%
Because then there would never be a reason to pay the school. $$
Just telling you fact that calculus is a hidden satanic agenda to divert the truth and some people don't like that you catch up the truth so it is made in crooked manner
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really correct.
It's all about the teacher. We all have been students, and we all know the difference between a good and bad teacher.
I finally totally understand this after 58 years !!! I did need to look up the definition of velocity and acceleration to completely understand this. When I was learning this, no internet, no TH-cam, no computers, just a single textbook and a library that more books that just drone on sayin the same thing that the teacher said. So if you didn't understand there was no new perspective or teaching methods. Thank God for Men and women like you with better teaching methods and a free medium to learn.
Wow, the best teacher on TH-cam. Am not an engineer, just wonder why most of the teachers can't explain calculous is a manner that kids or an average Jane like me can understand. Big thank you!!
Most teachers aren't teachers per say. They love the subject but just have no clue how to communicate it and a disgusting unwillingness to learn how to communicate. It is just easier to blame the student for not 'getting' it than learn how to teach 'it'.
@@martinaanandam3620 Most students who do not master basic math, has a high probability of finding difficulty in understanding calculus. I would suggest that they go back to the fundamentals of math like algebra, geometry, trigonometry, analytic geometry to have a good grasp on the concepts of calculus.
Best calculus teacher I ever had... Online
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@@user-ki6pt2zg1h good video, not sure how or why it applies to this calculus video, but thank you for sharing.
There are not bad students only bad teachers. These Teachers are excellent. All teachers in schools, colleges should undergo these teaching techniques, and they will take out the “terror “out from Calculus.
I dunno dude. I was a pretty bad student. :p
(You are right though... good teaching can make all the difference in the world.)
It's not only teachers who're to blame but students as well
There are obviously bad students.
I'd pay money to meet or even talk briefly with this man. He is the G.O.A.T of giving classes.
This is a man who has mastered the art of teaching.
connects the graphic representation to the definitions of velocity, acceleration... very simply and well. It's like math graphs meet physics.
I'm in 8th grade, and I decided to look up this course for fun. I actually got really into this and it makes so much sense. It would be so useful in HS! Thanks!
bro same
You are best teacher I had ever known! Amazing explanations! I am your student from now on...👍👍👍
It might help if you had used the units for position, velocity and acceleration in your graphs.
Most people do not understand the difference between these three because of the improper general use of the word ‘speed’. Restating the definition of the slope, as just a reminder, might help as well.
Also, would it not be better understood if the process was called something different than differentiation, which does not even hint as to what the process does, other than to say - ‘derived’ from.
If the act of differentiation always finds the slope, then call it ‘sloperation’ or ‘slopearate’ or ‘sloperization’ or ‘acquisition of slope’ or ‘slope derivation’.
Point taken on the units that’s actually a really good idea. Thank you very much appreciate it. Also I kind of like your names slopeorization and things like that I think they’re very clever in creative. However we need to use the word derivative simply because it’s all over the place in calculus and students really need to know how to use the proper terminology so that when they read textbooks and go into more advanced classes they understand the terminology.
Woooow, atleast ive gained something,this is dope,best calculus teacher online
Thanks be to God....I passed my problems
There is no god.
So grateful that you are sharing your insights and understanding of calculus. The way teach calculus is life changing. With respect. Thanks
Best teacher I have ever listened to
Great tutorial! BTW - acceleration and velocity ARE Rocket Science. Keep up the good work.
Good explanations! @Lloyd Welhelm, t is time, putting it in parentheses means a value is derived from the time value. IOW, if the time value is, say, 4, the function will produce a bigger value than if the time value is 2. That is to say, if you know the time, you can calculate the position.
A great gift to the learners.
You explain it so clearly, I think I can understand Einstein; Soon anyway.
Mate - you are an excellent teacher!
You are a great instructor. Thanks
Welcome!
Calculus is all about finding the individual components called dYs of a given whole called Y and summing (integrating) the given individual components = dYs to obtain the whole =Y.
The derivative = differential = dY = individual component of Y or WHOLE. Each component or dY is set dX apart where dX = 1/N (N being an indefinitely large number). The hypotenuse of the right triangle formed by sides dY and dX called dS, is the tangent and is an INDIVIDUAL straight line segment of the curve Y. It is NOT a point. All tangents are VECTORS (which a point cannot be)
As alluded above Integration is the continuous sum of the dYs (components) and obtaining Y (Whole).
Reminding me so much Sir, you touching all my favourite subject. differentiation wow I cant believe I’m feeling sitting in your class.
Clear as light. Congrats ! ❤ 👏
As a teacher. "Worth his weight in gold". Had I have had him as my tutor growing up, I could have been clever!. Thank you so much for abolishing the Misery and Mystery of Math, (3M) in all your sessions.
Kindest Regard
Francis Edge (UK).
If he were worth his weight in gold, that would be something. I would guess him to be around 170 pounds, which is 2,720 ounces. At today's gold rate (April 5, 2022) of $1,922 per ounce, that would be $5,227,840. A valuable teacher indeed.
First time understood. Many thanks.
Very good approach to maths.
So beautifully explained. Probably the best one I have seen so far. Thank you so much. Will probably will go through all your videos. Liked and subscribed. ❤
I never took calculus or wanted to major in engineering just because I constantly heard about the high failure rate. Now I regret it. If I had Jason tutor me, I might have just take calculus without fear of failing.
I lived in Galena Park years ago! Suburb of Houston. One thing about Houston...don't get in the wrong lane when you want to take an exit! You can put your blinker on but that will just make them tighten the gap! I would have to drive an extra 15-20 miles a few times since I got in the wrong lane! This was before GPS! Texas is a great state though!
I love the way teach .good advice thanks a lot.
Excellent lesson in basic differential calculus
Superb teaching!
“Calculus just sound mean” 😂😂, awesome teacher 🔥💪
Simply superb
Brilliant explaination, thank you!
You are the best
Thank you so much!
@@MathAndScience I have noticed something peculiar right at 3:56 min. The position with respect to time (distance in respect to time) starts at 0 for position and time. But the line with a slope represents the constant change of position (let's say 1 unit=100 ft/s) and of course time. But how ( let's say I am in a car) and with the begining of time and position at 0 suddenly I have traveled from 0 to the distance of 100 ft after 1 second without acceleration. If the second derivative shows me the accleration which is contsant of 2 m/s^2 than the first graph should show the start of the car with the constant speed at some point other than zero. The line should start at (let's say) at point 2 on the vertical axis which would represent 200 ft and after accelerating to the distance of 200 ft the car will not accelerate anymore and the second derivative would be correct. But in order to come up to constant speed you first must acclerate after a certain distance traveled. So, you can't start with 0 on the first graph and instantaneously travel with no acceleration without covering some distance. So, the the begining of the line p(t) should be drawn at least a part of unit (of distance that you accelerated) of position axis of more than zero if you start with zero seconds, too. At point zero you can't define neiither position nor time without acceleration first.
You are really really genius sir….
Any logarithmic relationship between integrated and differential form of function ???
So we get rid of lengthy calculation
I have noticed something peculiar right at 3:56 min. The position with respect to time (distance in respect to time) starts at 0 for position and time. But the line with a slope represents the constant change of position (let's say 1 unit=100 ft/s) and of course time. But how ( let's say I am in a car) and with the begining of time and position at 0 suddenly I have traveled from 0 to the distance of 100 ft after 1 second without acceleration. If the second derivative shows me the accleration which is contsant of 2 m/s^2 than the first graph should show the start of the car with the constant speed at some point other than zero. The line should start at (let's say) at point 2 on the vertical axis which would represent 200 ft and after accelerating to the distance of 200 ft the car will not accelerate anymore and the second derivative would be correct. But in order to come up to constant speed you first must acclerate after a certain distance traveled. So, you can't start with 0 on the first graph and instantaneously travel with no acceleration without covering some distance. So, the the begining of the line p(t) should be drawn at least a part of unit (of distance that you accelerated) of position axis of more than zero if you start with zero seconds, too. At point zero you can't define neiither position nor time without acceleration first.
You are very young here, see how mathematic makes you age quickly 🤔 it’s like the second derivative of acceleration X the velocity of time
That was beautiful! Thank you!
Great presentation
I knew NOBODY could teach me this except YOU...
Any percentage relationship between differential and integrated forms of function
So we don't required any lengthy calculation
Any coefficients of correlation between differential and integrated forms of same function ??
So we get rid of lengthy calculation
A glimmer of the light at the end of the tunnel.
Every teacher should be as good as you.
Thank you!!
Brilliant lecturer
@Jitu Brahmbhatt. Do not always put the blame to teachers. I don't agree with what you have said that there are not bad students only bad teachers. I want to remind you of the concept of "multiple intelligence". I do believe that there are people who are really good in Math but not that good in other fields. Also, there are some people who are really bad in Math but expert in other fields. Just saying... Thank you.
THANK YOU
THANK YOU... SIR...!!!
Thank you. Subscribed.
He 's the best.
Is the curve and t^2 in the curve expressing an approximation rather than a fact of acceleration? Sorry just trying to understand the relationships a bit better.
Thank you
wow thank you
It is not teacher'fault,nor text book writer.The clear conception of difference and fluxion are of utmost importance.I will make it clear soon,and thereby simplify thecalculus .
Where can I find the second part of this tutor??
Sir, I would like to do the lessons in order. Do you have a book that is published?
The best tutor ever 👍🏻👍🏻
LIAR!!!!!!
This is beautiful
Impresive...Now I am learning thanks and go on....
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what a man!!! 'like 3rd grade maths'
I've had you speaking Kiswahili my native language!. "Mambo jambo".
What book do you recommend for Calculus 1?
What is the definition of "a function" ??
how did you know in the example ;p(t)=t2 that the derivative is a straight light , i mean how can we know without using the law
ty
Mr Jason, why is it p(x)=t^2? Can't we change the exponent like p(x)=t^3?
Beautifully explained.
But I had one problem.
- Distance is a quadratic function of time, when velocity is changing uniformly, in other words Acceleration is constant. Therefore function of Distance with respect to Time will be "t square" (t 2). Understood.
- Velocity is changing linearly with time if acceleration is constant. That's why its a straight sloping line - a linear function. The slope of this line is the acceleration. It is a constant value. There Function of Velocity with respect to Time is a linear function. A "t" with it's coefficient as the "slope" which is actually the Acceleration.
This slope can be any value .. depending on the acceleration. Am I right?
Why did you use the numeral 2 as the example of its slope?
It creates a confusion, because Derivative of t 2 is indeed 2t (I have studied calculus in college) .. however if we go by looking at the slope as Acceleration is could be a 3 or a 4 (which we know is not the derivative of t square)..
It's not clear .. (head scratching student) .. this slope theory is not holding for student / viewer.
- However if we continue with the graph analogy we see that since Acceleration is constant .. a graph of Acceleration vs Time t being constant is a flat line parallel to t - axis with value of the 'slope' we found in the previous graph of Velocity Vs Time. In the example it was taken as 2 .. which is fine .. but it could be 3 or 4 or whatever numeral
Just pointing out a confusion that may occur for newbies encountering Derivatives for the first time.
Maybe I missed something! (It's been 30 years since I did any calculus at all .. I was here to look for Videos that would help my child with calculus)
THANKS.
@Jason Gibson
All are confused on the concepts of velocity and acc.n.First no one explains how to find derivative.
"It's gonna be like 3rd Grade math.."
*When you find 3rd Grade math hard*
Mixing a WHOLE lot of very very very very simple algebra concepts into this topic.... No one that hasn’t mastered those topics should be watching this video. Had to literally FFWD the video to the end to get 2 mins of useable info
Oh, my! I didn’t do well in third grade math.
how to prepare for my calculus exam? i feel fear already
very soft sounds
According to my math - based on the trajectory of the mortar I just fired - I'm on the wrong planet!
But for an increasing speed; the acceleration could also be increasing instead of being constant?
A vehicle can go from an acceleration of 2km.s-2 to 5km.s-2; for example
Yes absolutely the acceleration itself can be changing for example in a rocket launch.
@@MathAndScience Many thanks for your reply Professor. Appreciate it!
I have another confusion that i hope if you can give me a detailed clarification about; it's regarding why integration are considered to be the reverse of derivation (and vice-versa).
The second question: Is integration only used to calculate the area under a curve (of any given function) or for other purposes (and which purposes for example)? Plus what the area under the curve means mathematically and physically?
Many thanks;
At earliest stages
Bruh... Elon should feature your channel through his starlink, just saying... The world gotta know!
I could get behind that!!!
How long ago is this video? This is a younger Jason.
Thank you I know you and I stutter
the slope of the slope of the slope
See this video before YT remove it.
Thanks so much - its ok I plan to leave the video up for anyone who wants to learn.
Good morning eme
Is that your first board?
I'm 27 and this is the closest I have come to grasping derivatives.
Very nice
Sir where is the part 2 of this video ?
You have to subscribe to his course.
24:04 agree lol
you should have taught us how calculus formula has been proved or origin of calculus formula using simple example
first!!!!!
...and last
9:36 strange noise 😂
e looks younger here )
bønnemannen var her
HAHAHAHA
"It's really not rocket science."
Yet...
In school teachers are paid per hour that is why we can't get this kind of lectures ...hmm