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The Tangent Line and the Derivative (Calculus)
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- čas přidán 14. 08. 2024
- In calculus, you’ll often hear “The derivative is the slope of the tangent line.” But what is a tangent line? The definition is trickier than you might think.
Tangent lines are important because they are the best way to approximate a curve using a line. We can then use the slope of the line as a way to measure the “slope” of the curve.
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Written and Produced by Michael Harrison
Michael Harrison received his BS in math from Caltech, and his MS from the University of Washington where he studied algebraic number theory. After teaching math for a few years, Michael worked in finance both as a developer and a quantitative analyst (quant). He then worked at Google as a software engineer for over 5 years before leaving to found Socratica.
You can follow Michael on Twitter: / mlh496
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I love how you went over misconceptions of what a tangent line was first before giving the definition of it. Great video. :-)
Exactly.
That’s why math and other complicated topics lose people over time. We are given over simplified explanations which eventually fail us. Instead we should be taught the most accurate understanding. It may be harder to grasp initially, but when it is, will be worth the effort.
Great explanation. Calculus is fun when you actually know what's going on
Yeah mostly we don't know what are we doing 😂😂
Realest coment
My Calc professor taught the same way but his way was too complicated that I got lost lol. That’s why I am really happy someone did it this simple
"If you don't mind, I'd like to on a tangent and touch on an important point." lol
i love the effort you put to make the audience understand the concept of tangent crystal clear.
I want to thank you guys for your amazing videos; they are very well made! I just sent a letter to the UN asking them to ask other nations to subscribe. Hopefully, they'll send a letter to all nations imploring them to subscribe to your channel!
Now there is a guy who knows how to get things done. :) :)
Socratica he only knows how to get things done if the UN. comes through otherwise he gets nothing done.
I really like how you gave examples and then invited the viewer to try to come up with their own definition for a tangent line first. Hopefully you release some new math videos soon. Keep it up!
Thank you so much. The definitions with visuals made the Tangent Line and the Derivative easier to understand and appreciate.
Great vids. I really hope you don't stop making them. Specially next semester that I'm starting calculus
Thanks! We'll be making *many* more Calculus videos in the coming months.
where is the calc 3 and linear alegbra ones..
I just want to point out the sound design, I've never seen an educational video pay attention that. It was amazing
This is amazing, it made me understand the maths we take at school at a deeper level. Now it makes much more sense to me, thank you!
iam here from egypt wait for ur videos more than any of the lectures at my faculty of engineering ........keep going.......... :)
check out the
English Grammar Lessons
i think it's better for u to check out the Arabic vocabulary to know it is not great to use a different language from your main while speaking to mate of your country :)
nour khaled i already speak Arabic
i'm sure dude
We are so glad you are visiting us from Egypt! We dream of visiting one day! Thank you for watching and for your kind message. :)
This is so helpful and clear.it really saved me half and hour reading the textbook!
Squeaky clean explanation with succinct live demonstrations. Perfect teaching method!
I was going to make a video on the subject myself, until I saw this one... The fact that most definitions just talk about this tangent line touching the curve at 'one' point never really satisfied my hunger when looking at graphs. Great explanation, visuals and presentation pace.
Verry Verry good videos.
Thanks to Socratica team..........
Sir, your class is far above excellent.
This is amazing... Best explanation for tangent lines I have watched so far...
You're so kind, thank you for saying this! It really encourages us to make more videos.
A clear and comprehensive explanation enhanced with an extraordinarily good use of graphics.
greatest teacher I've encountered on CZcams. thank you so much
The great video made me consider subbing, and the end sealed it. Well done
WE GOT ONE!!!
We're so glad you've joined us! :)
I think this is the greatest explanation of a tangent line to a curve I've seen so far
Best explanation in CZcams. Made things so detailed and easy to understand. More such videos please. Thanks
One subscribe from India. Really your explanation are amazing.
I really love calculus and I understand the concepts, but as I teach the concepts to others, I wonder how it can be put best. This is likely the best video I've seen on introducing tangent lines and it was a great watch. Keep it up man!
The best ever explaination of derivatives. Absolute perfection.❤❤❤
thanks a ton for the awesome explanations and for making the videos available on CZcams
great video format , encourages the viewer to think, it's like a game , so creative , really really loved it
Sir, you may not believe that I have already thought of it in my school life. Thanks for this wonderful video. You really deserves like and subscribe.
Amusing,I really wanted such a video from somedays.I think it is the better channel for learning the fundamental....
Finally best channel to learn Mathematics. Keep adding more advance topics..........
This was simply amazing! I think I found my new favorite channel! ❤
You really answer all my freaking questions about tangent line
Thanks and I'll promote your video
very easily and neatly explained. Thanks
I have no idea by what do you mean by write a litter for me I found this channel by my search, and now I just realized it could be on of my best channels I ever found.
Creating free iraq 🇮🇶
It's amazing to see how to get deeper and deeper to the definition of tangent! Remind me how little I know about first principal😂
It makes a better approaching to understand concept better
Thanks so much Sir , first time, I am capable to understand what calculus actually is . Literally you gives understandable content and helping a lot of students.
Not going to skip adds cause you deserve it. Thank you very much
Thank you kind Socratica Friend! We appreciate your support! 💜🦉
please, more videos about calculus
Thank you so much, it made me, a thirteen year old, understand it very clear. (I'm Chinese)
We're so glad you're watching, Emily!! :D
This is great video I had ever seen. You opened my mind!!!
I love how it's so clear to understand!!
Great explanation I love it mas clear pa sa clear
Leibniz the co-founder of calculus gave the correct definition of a tangent line ie it touches a curve at 2 adjacent points separated by dx in the x direction and dy in the y direction, so it is dy/dx = the derivative or the hypotenuse of a right triangle = (dy^2+dx^2)^1/2
this avoids division by zero.
a single point cannot determine the direction of the tangent but dy/dx does
Avoids division by zero, but needs monads, which havnt been developed until middle of 20 century and overcomplicated, good replacement...
Could you please add videos on the vast topic of Integration?
It will help more.
I wish that my first college math class explained it this way. Nice job!
Where did the 6 come from. It seems as though it just appeared. Amazing video btw! 😊
I think I figured it out. The tangent line will eventually touch the curve at point (3,9). Therefore, the x value of point P (which is currently h) will either increase or decrease to 3 (it increases in this case as P is closer to the y axis). With that assumption, substituting h for 3 in the slope equation (m=h+3) gives you 6...
Might not be the 'right' way but it gets you there in this case :)
I love it! It's a crystal clear !
Thank u so much ♥️
Finally got what derivative and tangent line is
Thank you so much for the great explanation !! I will have an exam after two weeks, and needed this clarification!!
Sir, i will definitely recommend this channel to my friends.
Thank you so much!! We're so happy you've found our channel. When you share our videos with your friends, that really helps us grow. We really appreciate it!! :)
sir , you have conceptually explained it very well ,hope you will upload more videos
Perfect explanation👌
Very nice. Great video. The truth is that the derivative gives the definition of tangent line, not the other way around. For pedagogy purposes I think it's fine to tell students that the derivative is the slope of the tangent... as a way to get start since students start with some kind of intuitive "feeling" of tangent.
But the idea that derivative is "defined" to be the slope of the tangent is a misconception. The derivative is what it is. The tangent is defined as the line going through a point on the curve with the derivative of the curve at that point as its slope.
I NEED MORE VIDEOS! FORGOT MY CALC FROM 9 yrs AGO!!! SHOUT OUTS TO DERIVATIVES L'HOSPITAL!!!
AND*
I WANT TO BE A QUANT!!!
Dx/dy 4 lyfe
shared! like the idea of project 7B
WOW! This is incredibly well done.
really, great ... enjoyed so much... i 'll never mind subscribing.
Very Good Explanation.....
Plz Upload more topics of calculus.........
thank you! This Video was fabulous
Thanks A lot for making all my concepts clear!
Woah bro, u're such a legend at explaining.. plus the visual video is really super helpful ❤💙❤
Hello! This is truly a very good explanation of what a tangent really is. However, I could not help but notice that at 8:37 you said that in the formula m=dy/dx, dy and dx are differentials. I am sure you are aware of the following point but for the perfectionist viewer: In the derivative formula dy and dx ARE NOT DIFFERENTIALS. What holds is: f(x)'=(d/dx)y, where (d/dx) is an operator that changes f(x)=y. For the differentials: dy=f'(x)dx, which clearly does not mean that dy=f'(x)dx since dx can be 0. This might seem unimportant but there are a lot of instances in which it is crucial.
Interesting fact: Feynman, when young, invented his own symbol for the derivative just because he did not like Newton's notation: (dy/dx) because it commonly leads to the above misconception.
Cheers!
This channel make me a better person ^^
superb information. please keep more videos on calculus. i want know about subject
Awesome video …., 10 STAR ⭐️
I always had an interesting way of visualizing tangents. I think of the function like a path or road and the point is like a car driving in the road. The tangent is the direction of the exact moment that the car is going.
So my definition is that the tangent is the “acceleration” of the point at a given moment. Just to throw physics in the mix
Thank you so much for this! Teaching myself just for fun...
Some videos are not as clear
We love to see people learning because they're curious!! Thanks for watching!! 💜🦉
Good video. Why are people on the internet better than professors at university?
this was so helpful
thankyou
it helped me a lot
One word. Awesome!
This is awesome, the best I saw on this
Great videos! Could i ask you guys something? Could you gives us more of a basis on math talking about Analytical Geometry and René Descartes? Thanks
Explained Superbly..
This is so well explained. Thank you :D !
this was rlly well explained
Awesome! you made it simpler
The derivative is the slope of the tangent line right? So how can it be that the slope of the tangent line of y=x^2 = h+3 ( see 10:00) while the power rule gives 2x for the derivative?
In 6:42. How does the left hand and right side limit are not equal? (according to the graph) maybe im confused . Thank you.
Quality stuff!
Extrardinary explaination
Amazing
Realy good video. The only problem is - that tangent lines are not tangent lines. This cost me about week of afforting including try to use tangent circles - there are functions which intersect "tangent" line infinetly many times in every open ball, and even changing lines to circles not help. So, i conclude, that "tangent lines" rather rod or kernel lines then tangent. But i feel, that real truth in vector bundles, so going to study them.
Awesome Stuff, if you could do more videos on Definite integrals, Double , triple integrals & Differential equations etc. then that would make your channel crosses your goal (7 billion) ....!!
keep up your good work!
Pls keep posting....
superb content
Great work! Thanks a lot ✨
just perfect......awesome.....just too perfect....loved it.....
The sound effects are good because they make you follow along. Easy to get lost in math
Amazing explaination
thanks! very clear and enlightening;
Thanks very much
Thanks very much. Such an awesom video.
Thank you
Great video, but one mistake is at 6:03. The sinc function i.e. sin x / x ==> 1 when x =0. Mcclaurin series can be used to compute f(0). f(x) = sin (x)/x = [x - x^3/3! + x^5/5! ....] / x. ==> f(x) = 1 - x^2/3! + x^4/5! .... now we can see that we f(0) = 1.
Such a useful video!
Animations are amazing.
very nice > thank you