The Tangent Line and the Derivative (Calculus)

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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Пікірлер: 201

  • @q_q123
    @q_q1234 жыл бұрын

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

  • @sabashakeel0369

    @sabashakeel0369

    4 жыл бұрын

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

  • @tokkibunny8335

    @tokkibunny8335

    3 жыл бұрын

    Realest coment

  • @Siawash777

    @Siawash777

    2 жыл бұрын

    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

  • @mallorysmith1820
    @mallorysmith18207 жыл бұрын

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

  • @pinklady7184

    @pinklady7184

    3 жыл бұрын

    Exactly.

  • @arthurandrews113

    @arthurandrews113

    3 жыл бұрын

    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.

  • @sudhakarsiitm7982
    @sudhakarsiitm79822 жыл бұрын

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

  • @rafaelrincon3109
    @rafaelrincon31097 жыл бұрын

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

  • @slackbabo3858
    @slackbabo38585 жыл бұрын

    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!

  • @ElNietoPR
    @ElNietoPR7 жыл бұрын

    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

    @Socratica

    7 жыл бұрын

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

  • @tombates8093

    @tombates8093

    7 жыл бұрын

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

  • @petej011
    @petej0113 жыл бұрын

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

  • @fluffyrawan7656
    @fluffyrawan76565 жыл бұрын

    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!

  • @bartlx
    @bartlx2 ай бұрын

    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.

  • @sureshc4759
    @sureshc47597 жыл бұрын

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

  • @OzanYarman
    @OzanYarman3 жыл бұрын

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

  • @hemm2333
    @hemm23332 жыл бұрын

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

  • @SuHAibLOL
    @SuHAibLOL7 жыл бұрын

    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!

  • @coniferviveur3788
    @coniferviveur3788 Жыл бұрын

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

  • @sccm100
    @sccm1007 жыл бұрын

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

  • @Socratica

    @Socratica

    7 жыл бұрын

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

  • @JR1481M1

    @JR1481M1

    5 жыл бұрын

    where is the calc 3 and linear alegbra ones..

  • @namelessbrat7197
    @namelessbrat71978 ай бұрын

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

  • @fahadfaruqi203
    @fahadfaruqi2032 жыл бұрын

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

  • @dant7731
    @dant77314 жыл бұрын

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

  • @rajeshchandrasekharan3436
    @rajeshchandrasekharan34364 жыл бұрын

    Sir, your class is far above excellent.

  • @AllinOne-vd9oy
    @AllinOne-vd9oy6 жыл бұрын

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

  • @benjidamenji3428
    @benjidamenji34289 ай бұрын

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

  • @spencerwadsworth7024
    @spencerwadsworth70247 жыл бұрын

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

  • @Socratica

    @Socratica

    7 жыл бұрын

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

  • @alphapoint389
    @alphapoint3894 жыл бұрын

    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.

  • @SammaS14owo
    @SammaS14owo Жыл бұрын

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

  • @smit17xp
    @smit17xp3 жыл бұрын

    very easily and neatly explained. Thanks

  • @cloudyeight
    @cloudyeight6 жыл бұрын

    WOW! This is incredibly well done.

  • @LuisHernandez-if3dc
    @LuisHernandez-if3dc Жыл бұрын

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

  • @Vr-kl6yl
    @Vr-kl6yl5 жыл бұрын

    One subscribe from India. Really your explanation are amazing.

  • @subratprasadnayak6195
    @subratprasadnayak61956 жыл бұрын

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

  • @Ihasgun
    @Ihasgun Жыл бұрын

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

  • @samikakar2353
    @samikakar23532 жыл бұрын

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

  • @halaanbar-ko1ez
    @halaanbar-ko1ez5 ай бұрын

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

  • @olivewang961
    @olivewang9612 жыл бұрын

    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😂

  • @ahlalkubur
    @ahlalkubur2 жыл бұрын

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

  • @Socratica

    @Socratica

    2 жыл бұрын

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

  • @Dominic-su5pb
    @Dominic-su5pb3 жыл бұрын

    This is so well explained. Thank you :D !

  • @somenn.s3977
    @somenn.s39775 жыл бұрын

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

  • @peak_gaming_vibes
    @peak_gaming_vibes7 ай бұрын

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

  • @behnamyosufi3800
    @behnamyosufi3800 Жыл бұрын

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

  • @bismahaq6922
    @bismahaq6922 Жыл бұрын

    Thanks A lot for making all my concepts clear!

  • @nawaf_ksa0
    @nawaf_ksa03 жыл бұрын

    Great work! Thanks a lot ✨

  • @Carrymejane
    @Carrymejane4 ай бұрын

    I love it! It's a crystal clear !

  • @venjaminschuster2797
    @venjaminschuster27972 жыл бұрын

    thank you! This Video was fabulous

  • @nourkhaled7762
    @nourkhaled77627 жыл бұрын

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

  • @randomguy75

    @randomguy75

    7 жыл бұрын

    check out the English Grammar Lessons

  • @nourkhaled7762

    @nourkhaled7762

    7 жыл бұрын

    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

    @randomguy75

    7 жыл бұрын

    nour khaled i already speak Arabic

  • @nourkhaled7762

    @nourkhaled7762

    7 жыл бұрын

    i'm sure dude

  • @Socratica

    @Socratica

    7 жыл бұрын

    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. :)

  • @michellethapa3247
    @michellethapa32473 жыл бұрын

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

  • @YasirKhan-bl8lj
    @YasirKhan-bl8lj5 жыл бұрын

    Awesome! you made it simpler

  • @telakarapudemullu3257
    @telakarapudemullu32577 жыл бұрын

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

  • @freedomaugustus1555
    @freedomaugustus15552 жыл бұрын

    Woah bro, u're such a legend at explaining.. plus the visual video is really super helpful ❤💙❤

  • @MahmoodMuhenned
    @MahmoodMuhenned6 жыл бұрын

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  • @Theviswanath57
    @Theviswanath574 жыл бұрын

    This is awesome, the best I saw on this

  • @Carrymejane
    @Carrymejane4 ай бұрын

    It makes a better approaching to understand concept better

  • @RahulVerma-mj3dm
    @RahulVerma-mj3dm2 жыл бұрын

    Very Good Explanation.....

  • @shanu9837
    @shanu98376 ай бұрын

    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.

  • @ChetanSaini-rh9wf
    @ChetanSaini-rh9wf5 жыл бұрын

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

  • @johnhammer8668
    @johnhammer86687 жыл бұрын

    Thanks very much. Such an awesom video.

  • @amandeepsaha
    @amandeepsaha3 жыл бұрын

    thankyou it helped me a lot

  • @RK3868
    @RK38683 жыл бұрын

    this was rlly well explained

  • @nayeem150
    @nayeem1506 жыл бұрын

    Explained Superbly..

  • @AlessandroZir
    @AlessandroZir2 жыл бұрын

    thanks! very clear and enlightening;

  • @ifrancus9623
    @ifrancus96239 ай бұрын

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

  • @artofemong6148
    @artofemong61483 жыл бұрын

    Great explanation I love it mas clear pa sa clear

  • @FransiQ
    @FransiQ7 жыл бұрын

    Quality stuff!

  • @wick9462
    @wick94625 жыл бұрын

    Amazing explaination

  • @melancolicodeprofesion5695
    @melancolicodeprofesion56952 жыл бұрын

    Such a useful video!

  • @House_ssb
    @House_ssb7 жыл бұрын

    please, more videos about calculus

  • @omaryarali7805
    @omaryarali78055 күн бұрын

    Perfect explanation👌

  • @lonedruid1791
    @lonedruid17917 жыл бұрын

    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

  • @Saikumar-yamjala
    @Saikumar-yamjala7 жыл бұрын

    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!

  • @realcygnus
    @realcygnus7 жыл бұрын

    superb content

  • @AnshulChauhan95
    @AnshulChauhan953 жыл бұрын

    this was so helpful

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    @julioezequiel89357 жыл бұрын

    This channel make me a better person ^^

  • @emilyzhang4643
    @emilyzhang46436 жыл бұрын

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

  • @Socratica

    @Socratica

    6 жыл бұрын

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

  • @peaceoutt7339
    @peaceoutt73394 жыл бұрын

    Great video man 👍👍👍

  • @manuelgonzales2570
    @manuelgonzales25702 жыл бұрын

    Excellent!!

  • @AmitKuMunda
    @AmitKuMunda7 жыл бұрын

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

  • @sulaimansamatar4459
    @sulaimansamatar44594 жыл бұрын

    Thank you so much it really helped me underatand. and i hope you reach your goal i also subscribed. Though is been 3 yrs

  • @existentialcrisis9757
    @existentialcrisis97577 жыл бұрын

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

  • @Socratica

    @Socratica

    7 жыл бұрын

    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!! :)

  • @arianoori5924
    @arianoori59242 жыл бұрын

    One word. Awesome!

  • @mahit7
    @mahit7 Жыл бұрын

    Excellent!

  • @shreyasraut6224
    @shreyasraut62247 жыл бұрын

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

  • @comments_very_nice
    @comments_very_nice5 жыл бұрын

    Thanks a lot!

  • @huang47tw
    @huang47tw8 ай бұрын

    shared! like the idea of project 7B

  • @rajpurshinravasta990
    @rajpurshinravasta990 Жыл бұрын

    thank you!

  • @johnfrog9210
    @johnfrog92104 жыл бұрын

    Thanks very much

  • @nicolemelor7826
    @nicolemelor78262 жыл бұрын

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

  • @Socratica

    @Socratica

    2 жыл бұрын

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

  • @johnx5k
    @johnx5k2 жыл бұрын

    Awesome video …., 10 STAR ⭐️

  • @siriguna
    @siriguna6 жыл бұрын

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

  • @satishnatarajan
    @satishnatarajan7 жыл бұрын

    Marvelous!

  • @vamsidasyam9620
    @vamsidasyam96203 жыл бұрын

    Extrardinary explaination

  • @sadaqathussain9693
    @sadaqathussain96935 жыл бұрын

    Wahoooo....great work

  • @brendamg7298
    @brendamg72982 жыл бұрын

    Thank you

  • @mdashfakuzzamanchy5218
    @mdashfakuzzamanchy52182 жыл бұрын

    wow. just wonderful

  • @Ph.student6
    @Ph.student63 ай бұрын

    very nice > thank you

  • @numbercollage5450
    @numbercollage54504 жыл бұрын

    Animations are amazing.

  • @SkyeMpuremagic
    @SkyeMpuremagic Жыл бұрын

    Thank you so much for this! Teaching myself just for fun... Some videos are not as clear

  • @Socratica

    @Socratica

    Жыл бұрын

    We love to see people learning because they're curious!! Thanks for watching!! 💜🦉

  • @parveensabir4729
    @parveensabir47294 жыл бұрын

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

  • @qualquan
    @qualquan5 жыл бұрын

    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

    @epuremath

    11 ай бұрын

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

  • @neesaali803
    @neesaali8033 жыл бұрын

    Thanks 🙏

  • @tommijones8095
    @tommijones80955 жыл бұрын

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

  • @benchiama3146

    @benchiama3146

    3 жыл бұрын

    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 :)

  • @theupscpost8389
    @theupscpost83897 күн бұрын

    Amazing

  • @otakurocklee
    @otakurocklee3 жыл бұрын

    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.