The Tangent Line and the Derivative (Calculus)

[@mallorysmith1820]

I love how you went over misconceptions of what a tangent line was first before giving the definition of it. Great video. :-)

[@pinklady7184]

Exactly.

[@arthurandrews113]

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.

[@q_q123]

Great explanation. Calculus is fun when you actually know what's going on

[@sabashakeel0369]

Yeah mostly we don't know what are we doing 😂😂

[@bloomsxobini]

Realest coment

[@Siawash777]

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

[@sudhakarsiitm7982]

i love the effort you put to make the audience understand the concept of tangent crystal clear.

[@rafaelrincon3109]

"If you don't mind, I'd like to on a tangent and touch on an important point." lol

[@bartlx]

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.

[@fahadfaruqi203]

I just want to point out the sound design, I've never seen an educational video pay attention that. It was amazing

[@slackbabo3858]

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!

[@petej011]

Thank you so much. The definitions with visuals made the Tangent Line and the Derivative easier to understand and appreciate.

[@Ihasgun]

I think this is the greatest explanation of a tangent line to a curve I've seen so far

[@ElNietoPR]

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!

[@Socratica]

Now there is a guy who knows how to get things done. :) :)

[@tombates8093]

Socratica he only knows how to get things done if the UN. comes through otherwise he gets nothing done.

[@benjidamenji3428]

greatest teacher I've encountered on KZbin. thank you so much

[@somenn.s3977]

Finally best channel to learn Mathematics. Keep adding more advance topics..........

[@coniferviveur3788]

A clear and comprehensive explanation enhanced with an extraordinarily good use of graphics.

[@rajeshchandrasekharan3436]

Sir, your class is far above excellent.

[@OzanYarman]

Squeaky clean explanation with succinct live demonstrations. Perfect teaching method!

[@fluffyrawan7656]

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!

[@AllinOne-vd9oy]

Verry Verry good videos. Thanks to Socratica team..........

[@ahlalkubur]

This is amazing... Best explanation for tangent lines I have watched so far...

[@Socratica]

You're so kind, thank you for saying this! It really encourages us to make more videos.

[@MGB-wz3jz]

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?

[@nourkhaled7762]

iam here from egypt wait for ur videos more than any of the lectures at my faculty of engineering ........keep going.......... :)

[@randomguy75]

check out the English Grammar Lessons

[@nourkhaled7762]

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 :)

[@randomguy75]

nour khaled i already speak Arabic

[@nourkhaled7762]

i'm sure dude

[@Socratica]

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. :)

[@sccm100]

Great vids. I really hope you don't stop making them. Specially next semester that I'm starting calculus

[@Socratica]

Thanks! We'll be making *many* more Calculus videos in the coming months.

[@JR1481M1]

where is the calc 3 and linear alegbra ones..

[@alphapoint389]

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.

[@arbitrarylib]

The sound effects are good because they make you follow along. Easy to get lost in math

[@jessicaaaaa7728]

This is so helpful and clear.it really saved me half and hour reading the textbook!

[@peak_gaming_vibes]

The best ever explaination of derivatives. Absolute perfection.❤❤❤

[@huang47tw]

shared! like the idea of project 7B

[@hemm2333]

Best explanation in KZbin. Made things so detailed and easy to understand. More such videos please. Thanks

[@SammaS14owo]

You really answer all my freaking questions about tangent line Thanks and I'll promote your video

[@shanu9837]

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.

[@halaanbar-ko1ez]

great video format , encourages the viewer to think, it's like a game , so creative , really really loved it

[@smit17xp]

very easily and neatly explained. Thanks

[@otakurocklee]

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.

[@Vr-kl6yl]

One subscribe from India. Really your explanation are amazing.

[@qualquan]

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

[@epuremath]

Avoids division by zero, but needs monads, which havnt been developed until middle of 20 century and overcomplicated, good replacement...

[@doomed5206]

Probably the best video I have seen in my lyf. Damn you touched so many points.

[@subratprasadnayak6195]

Amusing,I really wanted such a video from somedays.I think it is the better channel for learning the fundamental....

[@ifrancus9623]

I wish that my first college math class explained it this way. Nice job!

[@sureshc4759]

thanks a ton for the awesome explanations and for making the videos available on KZbin

[@LuisHernandez-if3dc]

I love how it's so clear to understand!!

[@Carrymejane]

It makes a better approaching to understand concept better

[@ChetanSaini-rh9wf]

Could you please add videos on the vast topic of Integration? It will help more.

[@olivewang961]

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😂

[@spencerwadsworth7024]

The great video made me consider subbing, and the end sealed it. Well done

[@Socratica]

WE GOT ONE!!! We're so glad you've joined us! :)

[@House_ssb]

please, more videos about calculus

[@georgevlassis3515]

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!

[@namelessbrat7197]

This was simply amazing! I think I found my new favorite channel! ❤

[@SuHAibLOL]

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!

[@nicolemelor7826]

Not going to skip adds cause you deserve it. Thank you very much

[@Socratica]

Thank you kind Socratica Friend! We appreciate your support! 💜🦉

[@kelvinadimas8851]

math is fun whenever u can visualize it

[@emilyzhang4643]

Thank you so much, it made me, a thirteen year old, understand it very clear. (I'm Chinese)

[@Socratica]

We're so glad you're watching, Emily!! :D

[@existentialcrisis9757]

Sir, i will definitely recommend this channel to my friends.

[@Socratica]

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!! :)

[@zacktrever1878]

I NEED MORE VIDEOS! FORGOT MY CALC FROM 9 yrs AGO!!! SHOUT OUTS TO DERIVATIVES L'HOSPITAL!!!

[@zacktrever1878]

AND*

[@zacktrever1878]

I WANT TO BE A QUANT!!!

[@zacktrever1878]

Dx/dy 4 lyfe

[@artofemong6148]

Great explanation I love it mas clear pa sa clear

[@autodidactusplaysjrpgs7614]

Good video. Why are people on the internet better than professors at university?

[@parveensabir4729]

Plz Upload more topics of calculus.........

[@dant7731]

This is great video I had ever seen. You opened my mind!!!

[@michellethapa3247]

Thank u so much ♥️ Finally got what derivative and tangent line is

[@MahmoodMuhenned]

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 🇮🇶

[@Carrymejane]

I love it! It's a crystal clear !

[@omaryarali7805]

Perfect explanation👌

[@samikakar2353]

sir , you have conceptually explained it very well ,hope you will upload more videos

[@cloudyeight]

WOW! This is incredibly well done.

[@NicoleJulianaHamsirani]

Why does when h approaches 3 the m also approaches 6? How? 10:09

[@MRSDR100]

For the final definition 9:18

[@Lailalilly07]

LIFE SAVER! عمو بحبك❤

[@RahulVerma-mj3dm]

Very Good Explanation.....

[@nayeem150]

Explained Superbly..

[@steveann9705]

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.

[@teronchapman6326]

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.

[@teronchapman6326]

So my definition is that the tangent is the “acceleration” of the point at a given moment. Just to throw physics in the mix

[@RK3868]

this was rlly well explained

[@blackfox111]

7:04 Isnt dy/dx is supposed to be 0 ?

[@joemarbabon4314]

In 6:42. How does the left hand and right side limit are not equal? (according to the graph) maybe im confused . Thank you.

[@ninjaker]

If they are not equal then there is simply no limit

[@Theviswanath57]

This is awesome, the best I saw on this

[@julioezequiel8935]

This channel make me a better person ^^

[@vamsidasyam9620]

Extrardinary explaination

[@tommijones8095]

Where did the 6 come from. It seems as though it just appeared. Amazing video btw! 😊

[@bodaciousJaban]

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 :)

[@bismahaq6922]

Thanks A lot for making all my concepts clear!

[@AmitKuMunda]

really, great ... enjoyed so much... i 'll never mind subscribing.

[@YasirKhan-bl8lj]

Awesome! you made it simpler

[@behnamyosufi3800]

Thank you so much for the great explanation !! I will have an exam after two weeks, and needed this clarification!!

[@Jeff-fc7nf]

This video reminds me of why I dont like math. Everything is in reference to this "line", I dont understand what this line is and what determines its slope. The slope changes as it slides around, what determines the slope of the line at any given point. My issue with math and most instructions on science is about so many other things that whatever is trying to be explain that it takes me like 10 times longer to understand anything. When taking physiology class, there are a few weeks spent on this idea called Action potential. Worst name to describe anything, and then people say its like electricity and they want you to memorize all these voltages and ions and so forth. So I set out on my own to try and learn it. Took me three weeks when it finally clicked and suddenly I understood why no one can teach it, they dont understand it. Sure everyone can memorize the steps but they have no idea whats going on. Action potential is the one way directional propagation of a change in polarity of the surface molecules that make up a neuron. Literally if anyone would have just told me that first, then It would have been so much easier to grasp all the nuance steps, but for me I cant memorize steps first. I must understand the concept before my brain will accept the steps. For some reason educators do this backwards. They want you to grind the steps over and over and then hope you get the concept later. Im sure this is a great video for most people but I feel more confused about this then I did when I first googled it.

[@amandeepsaha]

thankyou it helped me a lot

[@epuremath]

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.

[@venjaminschuster2797]

thank you! This Video was fabulous

[@johnx5k]

Awesome video …., 10 STAR ⭐️

[@theupscpost8389]

Amazing

[@NikeJustDoItBeaverton]

Please More Videos .... And Please let me know what is the software you use to get those animation of equation

[@AnshulChauhan95]

this was so helpful

[@wick9462]

Amazing explaination

[@telakarapudemullu3257]

superb information. please keep more videos on calculus. i want know about subject

[@sahailiash2108]

please explain how can we get slope at each point of curve?

[@lonedruid1791]

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

[@shreyasraut6224]

just perfect......awesome.....just too perfect....loved it.....

[@sniggychan9279]

Why curve's point is deffentiable at touching point ?

[@arianoori5924]

One word. Awesome!

[@ellabrendairianto5211]

This helps more than school

[@numbercollage5450]

Animations are amazing.

[@AlessandroZir]

thanks! very clear and enlightening;

[@Dominic-su5pb]

This is so well explained. Thank you :D !

[@losdiasdeluis]

Such a useful video!