Derivative as a concept | Derivatives introduction | AP Calculus AB | Khan Academy

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  • เผยแพร่เมื่อ 30 ม.ค. 2025

ความคิดเห็น • 357

  • @fluffyrawan7656
    @fluffyrawan7656 6 ปีที่แล้ว +2196

    Our teachers teach us how to pass calculus exams, not calculus itself. Thank you.

    • @AaBb-qs6gh
      @AaBb-qs6gh 4 ปีที่แล้ว +106

      I agree , but for schools since they are limited by time, sometimes you need to study to pass not to understand😆
      You can understand in your free time which we don't have😁

    • @baticadavinci3984
      @baticadavinci3984 4 ปีที่แล้ว +8

      couldn't agree more!

    • @unknownunknowns
      @unknownunknowns 4 ปีที่แล้ว +6

      Aa Bb It looks like graduating high school at 18 is really early...

    • @Devilfish4387
      @Devilfish4387 3 ปีที่แล้ว +3

      true and sad

    • @kgtech6882
      @kgtech6882 3 ปีที่แล้ว +10

      @@AaBb-qs6gh i mean, in this 7 minutes i already learned so much than 1 and a half hour in a class.

  • @Hot-Dog-Racing
    @Hot-Dog-Racing 7 ปีที่แล้ว +575

    I wish more teachers and professors would teach math like this with actually relating it to the graph rather than just going straight into how to calculate it. It would be so much easier to learn this then focus on the actual math of it. This makes way more sense than just starting directly with "find dy/dx of sin^2(12x)/tan(18x) or some seemingly-arbitrary crap like that. Thank you!

    • @infinitymfg5397
      @infinitymfg5397 7 ปีที่แล้ว +3

      I agree.

    • @luxfries1524
      @luxfries1524 3 ปีที่แล้ว +2

      Learn trigonometry

    • @luxfries1524
      @luxfries1524 3 ปีที่แล้ว +5

      Nvm this was 3 years ago

    • @fraddi
      @fraddi 3 ปีที่แล้ว

      CALCULUS WAS INVENTED IN INDIA. THE EUROPEANS STOLE IT.

    • @alkazi1482
      @alkazi1482 2 ปีที่แล้ว +2

      @@fraddi And how does it help, you know the invention of the wheel was not achivement that happened in one place, it happened multiple place. Calculus is one of the primary way to calculate. Why couldn't it be discovered in multiple areas of the glove. The chinese also discovered calculas. Calculas isn't invented, it was discovered.

  • @omniscienceisdead8837
    @omniscienceisdead8837 3 ปีที่แล้ว +298

    Within the first 3 minutes I understood more than the 3 months I've been studying in my college, you guys are doing God's work

    • @razalasreficul6902
      @razalasreficul6902 ปีที่แล้ว +13

      Clearly more like "you guys are doing my professors' work"

  • @superawesomecaptainmcfluff9506
    @superawesomecaptainmcfluff9506 7 ปีที่แล้ว +789

    In India, we're taught to practise a million derivative calculus sums without knowing it's beauty or use, you have really opened my eyes to its practicality and concept. Thanks.
    P.S - Think about partnering with Numberphile for a video please!

    • @r.s.banimations561
      @r.s.banimations561 6 ปีที่แล้ว +48

      Don't say in INDIA .say it as "in your school or college .

    • @resurgam2243
      @resurgam2243 6 ปีที่แล้ว +58

      @@r.s.banimations561 In most schools.

    • @viveksukhla8631
      @viveksukhla8631 6 ปีที่แล้ว +40

      @@r.s.banimations561 in every school

    • @parulaggarwal9405
      @parulaggarwal9405 6 ปีที่แล้ว +2

      👌👌

    • @aarohansharma4551
      @aarohansharma4551 5 ปีที่แล้ว +39

      It's correct to a large extent...... I know students who excel at calculus(solving sums) but don't even know what it means conceptually!

  • @ceejay1684
    @ceejay1684 3 ปีที่แล้ว +68

    saved my life on this one. teachers just kept throwing formulas and methods of finding derivatives without explaining what derivatives are themselves. thank you, saul

    • @bladeiron
      @bladeiron 9 หลายเดือนก่อน +2

      Your teacher is stuck in the 1950s, because that is what a lot of teachers did before the Calculus Reform of what I believe was in the 1980s.

  • @darthmmc7660
    @darthmmc7660 17 วันที่ผ่านมา +4

    Pretty crazy how I've been doing derivatives for two years, getting good marks on those exams, but I didn't fully understand the very concept of them until now. Great video.

  • @theopenacademy9102
    @theopenacademy9102 6 ปีที่แล้ว +95

    Khan I really got to thank you for the work youve done! Ive been out of high school for over three years, time i took off to travel and learn skills I was curious about and I have finally decided to attend university this september and I have calc and physics as a major part of the program that I got into and I had forgotten practically everything I learned in high school. I have spent the last two months doing about 7 hours of khan academy a day and for the first time in my life I absolutely love math and physics. Dont get me wrong i did well in highscool math etc... but I didnt understand a thing. I was schooled but I wasnt educated. Taught concepts with no effort in establishing intuition. All the courses that I enjoyed the most in highschool were english, history, social sciences etc.. as most of the learning in those classes is about intuition and critical thinking while all science and math courses were all blind applications. Thank you so much! I have learned more than just math and physics concepts from you but the right way to teach and to educate! So much love!!

    • @Aritul
      @Aritul 3 หลายเดือนก่อน +2

      What a wonderful, appreciative comment!

  • @ameesinghamazing3825
    @ameesinghamazing3825 ปีที่แล้ว +10

    THIS IS THE KIND OF TEACHERS OUR WORLD NEEDS! teachers who are energetic, and have a depth of knowledge. it has been rightly said and holds true," teachers who love to teach, teach children to love learning!"

  • @uniqueh5203
    @uniqueh5203 4 ปีที่แล้ว +35

    I'm a master graduate in the faculty of architecture and I can say, it is by far the best explained differential concept lesson I have ever seen in my life !

  • @randyshi72
    @randyshi72 2 ปีที่แล้ว +26

    This really helped me understand the true concept of derivatives, not just a bunch of formulas. Thank you so much!

  • @joedimon
    @joedimon 3 ปีที่แล้ว +8

    Just failed my Math Content Praxis and have been feeling really depressed for three days over it. But this video just made me happy again! You really have to find the easiest way for you to engage with the material, for me it's just sitting back and watching Khan teach.

  • @LoganSnyder
    @LoganSnyder 5 ปีที่แล้ว +8

    I've never learned calculus in my life and now I'm a college senior in a machine learning class that DID NOT HAVE any math prerequites, and all the sudden the professor springs calculus on us like we're supposed to know it. Oof. This videos are saving me right now, haha. Thank you!

    • @15justt
      @15justt 4 ปีที่แล้ว

      How are you in a course with machine learning and no calculus lmao

    • @LoganSnyder
      @LoganSnyder 4 ปีที่แล้ว +6

      @@15justt Like I said the university never put math prerequisites on the course which was pretty dumb. I'm happy to say I passed the class with an A though. I hardly slept during the Spring 2020 semester haha

    • @15justt
      @15justt 4 ปีที่แล้ว +1

      @@LoganSnyder same... Coincidentally what kept me up at night was Calculus 2 😂

  • @kartikeyekhanna2657
    @kartikeyekhanna2657 7 ปีที่แล้ว +8

    Dear Khan Academy!
    Your videos have proved to be the most helpful!! Please post more videos on calculus now!

  • @MichiganPeatMoss
    @MichiganPeatMoss 3 ปีที่แล้ว +2

    Stuffed away since some time in a 1988 college class, brought out and clarified in 2022. Many thanks.

  • @Tom-sq2nt
    @Tom-sq2nt 2 ปีที่แล้ว +5

    Thank you, it finally make me understand what is derivative. My teacher said the concept wasn't important so she only teach us how to do the exercise

  • @ellastevens5638
    @ellastevens5638 2 ปีที่แล้ว +7

    Explained in a way that was easy to understand and very helpful for my exam, thank you so much!! I used KA back in middle school and at the time didn't realize how many videos there were over so many topics, now that I have this is going to be a great help for this college student!

  • @geektoys370
    @geektoys370 11 วันที่ผ่านมา +1

    I learnt so much from this guy.

  • @swarajrajpure8073
    @swarajrajpure8073 7 ปีที่แล้ว +45

    Thank you so much Khan Academy! You people are the best in convincing us the tough concepts easy way!

    • @fraddi
      @fraddi 3 ปีที่แล้ว

      CALCULUS WAS INVENTED IN INDIA. THE EUROPEANS STOLE IT.

  • @zoombae
    @zoombae 7 ปีที่แล้ว +868

    Is it weird that I Have a slight crush on this man

  • @mohamedaminebaccar8095
    @mohamedaminebaccar8095 3 ปีที่แล้ว +14

    I finally understood derivative after 3 MONTHS of studying it at class
    You literally saved my life
    Huge thanks 🙏

  • @MeinCouch123
    @MeinCouch123 2 ปีที่แล้ว

    dude, I feel like this is the first time this has made any sense- none of my teachers ever mentioned how dy/dx relate to a graph or the tangent line AT ALL, they just name drop terms without explaining.

  • @gouisedeau
    @gouisedeau 5 ปีที่แล้ว +30

    thought he was playing Counter-strike ..... BTW excellent tutorial, reminder

  • @yummytacos3357
    @yummytacos3357 4 หลายเดือนก่อน +1

    ngl it's these old gems that rlly carry me through calculus

  • @jadesanjose2520
    @jadesanjose2520 4 ปีที่แล้ว +6

    So many a-ha moments... thank you for explaining the things that would seemingly be useless. For example, the definition of delta... that made it all click for me. It's just like the slope formula! I understand why they want us to think about it differently to not get concepts confused but a simple comparison is helpful with using the knowledge we already have and to build on it. I take online classes and the video instructor just kept saying "delta y" and "delta x" which is meaningless to me! Now it all makes sense though. I appreciate that you do this in all your videos. Sometimes I'm like omg its such a long video but well worth it for those like me who LIKE to understand the "whys?" no pun intended... :)

  • @RicardoMartinez-jy5lo
    @RicardoMartinez-jy5lo 2 ปีที่แล้ว +1

    I took my high school math late as an adult in a community college; so this explanation is very much understandable to me as someone not gifted at all for Math.

  • @alessandromalfa3919
    @alessandromalfa3919 2 ปีที่แล้ว +1

    i am from italy. THANK YOU FOR ALL YOUR GREAT JOB!!!! my teacher made me get confused about this interesting subject, but you cleared my mind. Thanks

  • @fatimah.tulkubra2447
    @fatimah.tulkubra2447 5 หลายเดือนก่อน

    Khans academy is the best academy to learn mathematics... I always love to watch videos on Khan academy

  • @indecisive5546
    @indecisive5546 หลายเดือนก่อน +1

    Now I can use this info to humble the calculus kids in math tutoring😈

  • @keepfeatherinitbrothaaaa
    @keepfeatherinitbrothaaaa 3 หลายเดือนก่อน

    This is the first video that made the idea click with me. Thank you so much.

  • @Jesse_The_Lazy
    @Jesse_The_Lazy 2 ปีที่แล้ว +1

    You did the impossible. I learned a little bit of calculas. Thank you :)

  • @matteobiancardi9581
    @matteobiancardi9581 2 หลายเดือนก่อน

    great material, really, I'm not surprised the channel is so famous

  • @maskedmarvyl4774
    @maskedmarvyl4774 ปีที่แล้ว +3

    The reason the slope line here is also called the "secant line", is because as per geometry, it is a line that intersects a circle (or curve) at a minimum of two points. I don't know if it is being used here to also describe the secant function in trigonometry, i.e. the hypotenuse of a triangle divided by its adjacent side.

  • @TimePass-jr7pj
    @TimePass-jr7pj 4 หลายเดือนก่อน

    Wow !!!!
    Today I actually understood what the derivative really is !!
    This is a lot more interesting than the college's boring class

  • @quriositysquared1028
    @quriositysquared1028 7 ปีที่แล้ว +6

    You sir, are saving lives(trust me on this one!).

  • @paulaan881
    @paulaan881 4 ปีที่แล้ว +7

    GOOD TEACHER!!! YOU MADE ME FALL IN LOVE WITH MATH ... Gracias

  • @E7R1I6C
    @E7R1I6C 3 ปีที่แล้ว +28

    Lol imagine if teachers explained the building blocks instead of just giving you problems. A year of calc in college and never actually understood it, just learned how to pass tests

    • @polla2256
      @polla2256 2 หลายเดือนก่อน

      Exactly my thoughts. It would take no more than a few weeks to get a fundamental understanding for degree level maths. At school my teachers were terrible, in the army when actual engineers taught me I cruised through this stuff going as far as fluid dynamics.

  • @tthproductions8076
    @tthproductions8076 7 ปีที่แล้ว +12

    Im using khanacademy rght now :)

  • @asparagus7014
    @asparagus7014 11 หลายเดือนก่อน +1

    I love math, but the teachers explain it at such a fast rate that I can't keep up.

  • @anmolrattansinghsidhu1938
    @anmolrattansinghsidhu1938 4 หลายเดือนก่อน

    I completely forgot Calculus after school/university. Used this lecture for the calculus in my CFA. Thanks Khan academy.

  • @karllatraverse6772
    @karllatraverse6772 หลายเดือนก่อน

    I did the classed and really tried hard but then forgot after my last exam. It's nice make myself remember again

  • @MGTMusic
    @MGTMusic 2 ปีที่แล้ว

    Thank you ! Thank you ! Thank you ! God bless you!!!

  • @niyonezabernard6045
    @niyonezabernard6045 6 หลายเดือนก่อน

    I wish I would see him. He puts am end when I feel he is continues. He is a just phenomenon.

  • @Kate-zz4nk
    @Kate-zz4nk 2 ปีที่แล้ว +1

    You explained this extremely well! It actually makes sense now

  • @DeadMindSociety
    @DeadMindSociety หลายเดือนก่อน

    Eureka! It suddenly clicks now! This simple plain talking explanation ties it together in 7 minutes. Now I understand all the fuss about learning how to work with limits. As you approach the limit you begin to solve for the slope of the line at that limit. I think...

  • @proudamazighian9334
    @proudamazighian9334 2 ปีที่แล้ว

    The first and already the best math channel I found

  • @princessEA7
    @princessEA7 9 หลายเดือนก่อน

    Very good in-depth explanations in this channel! Thank you very much!

  • @nickh.44
    @nickh.44 4 หลายเดือนก่อน

    Here i am trying to learn math concepts even though i have finished math all the way up to differential equations (i even passed with a A). However i feel like school stresses practice problems and not concepts. Which is strange bc if i understood the concepts maybe the classes would have been easier. So thanks, bc this actually makes so much more sense now than when i originally learned it

  • @caratinawaiters2590
    @caratinawaiters2590 ปีที่แล้ว

    Your excitement in this video is breathtaking

  • @swiftbifo17
    @swiftbifo17 หลายเดือนก่อน +2

    I should’ve watch this when I was in 7th grade 😭
    (I was getting tortured).

  • @frankenstein3397
    @frankenstein3397 3 ปีที่แล้ว +1

    this explanation clears my dy/dx doubt,thanks.

  • @WhovianRanger42
    @WhovianRanger42 ปีที่แล้ว

    It's actually a lot of fun to practice my English listening with Math videos! :)

  • @vadrif-draco
    @vadrif-draco 2 ปีที่แล้ว

    That cursor and in general those illustration tools are so impressive!

  • @LeonardoDelCarpioBellidoVargas
    @LeonardoDelCarpioBellidoVargas ปีที่แล้ว

    THANK YOU!!! FINALLY!!! I'M GETTING ANSWERS!!

  • @millenial1986
    @millenial1986 ปีที่แล้ว

    Not all heroes wear capes - best explanations for given topics you can find - simple, clear, and on point. Thanks for making math interesting and understandable to everybody

  • @benv5115
    @benv5115 8 หลายเดือนก่อน

    You're a national hero!

  • @johnnamtae9610
    @johnnamtae9610 4 ปีที่แล้ว +2

    Your handwriting is so good in these.

  • @khalilgueye5097
    @khalilgueye5097 2 ปีที่แล้ว

    i have nobody to thank for where i am in life, but you, sal khan

  • @melsitler
    @melsitler ปีที่แล้ว

    I'm about to start derivatives in my calculus class and I always have to know WHY I'm learning something or I won't want to learn it. THANK YOU!

  • @ValidatingUsername
    @ValidatingUsername 8 หลายเดือนก่อน

    To maintain the axiom of RS = LS it should be reinforced that d/dx y or f(x) is literally y’ and f’(x) respectively.
    d/dx F(x) = f(x) = int{ f’(x) dx
    F(x) = int{ f(x) dx = int{ f’(x) dx^2
    d/dx^2 F(x) = d/dx f(x) = f’(x)
    To further that notion, as above, the integral sign and dx are just brackets and uSub is a change of base for the brackets.

  • @josephajoseph9535
    @josephajoseph9535 ปีที่แล้ว

    Give this man a manhatten project!❤

  • @hotball5361
    @hotball5361 2 ปีที่แล้ว

    Definition of derivatives in this is very understandable and very practically explained.THANKYOU.

  • @michio028yt8
    @michio028yt8 10 หลายเดือนก่อน

    thaks you you teached me enought to continue learning

  • @diegoespinoza8997
    @diegoespinoza8997 ปีที่แล้ว

    Could you believe me if I told you that I only now understand the concept of a derivative? And all I had to do was to search for the answer in English? Idk how, but I don't grasp these concepts when I am being taught in Spanish, which ironically, is my mother language, thank you very much for this "humanitarian service", lol.

  • @bibauu
    @bibauu ปีที่แล้ว

    i learnt more in this video abt deriv than 3 years of high school

  • @DylanWoods-kw6km
    @DylanWoods-kw6km 11 หลายเดือนก่อน

    I'm in 7th grade teaching my self calculus TH-cam is the best

  • @TahiraZubair-t3o
    @TahiraZubair-t3o 6 หลายเดือนก่อน

    My favorite course 😊

  • @rajib05555
    @rajib05555 7 หลายเดือนก่อน

    Excellent video thanks a lot!!

  • @megancower1884
    @megancower1884 6 ปีที่แล้ว +5

    Wow. I feel things are about to click.

  • @conradkotze4615
    @conradkotze4615 2 ปีที่แล้ว

    This makes so much more sense!

  • @meloniejen8400
    @meloniejen8400 5 ปีที่แล้ว +7

    Amount of likes is the amount of lives Khan has saved

  • @piyushpandey2480
    @piyushpandey2480 3 หลายเดือนก่อน

    Exceptional explanation

  • @ЮлияШтундюк
    @ЮлияШтундюк 2 ปีที่แล้ว

    Finally got it, thank you for insight!

  • @justinkim7202
    @justinkim7202 ปีที่แล้ว

    Loving these lessons!

  • @vatsayana2004
    @vatsayana2004 2 ปีที่แล้ว

    My college professors had no knowledge about derivatives, Limits, Calculus and Integration. They were crammers and skilled workers and unnecessarily getting big salary.

  • @fataldreidel5846
    @fataldreidel5846 4 ปีที่แล้ว

    imagine knowing why people in ancient times needed to invent ways to discover the derivative.....that might form a lot more connections and motivate people to care more about learning this stuff. -Former math study

    • @rajdeepsindhu9268
      @rajdeepsindhu9268 4 ปีที่แล้ว

      Absolutely!
      In fact, Grant Sanderson, owner of 3Blue1Brown takes this very approach in his "Essence of Calculus" series. He describes his primary goal as giving the viewers a feeling that they too could have stumbled upon these situations and have invented calculus themselves.

  • @phatphan1403
    @phatphan1403 3 ปีที่แล้ว

    I would have Aced all my AP classes back in 2005 if TH-cam instruction videos have existed back then.

  • @krishnaca65
    @krishnaca65 9 หลายเดือนก่อน

    very nicely explained sir.

  • @abhyudayaaware8653
    @abhyudayaaware8653 3 ปีที่แล้ว +1

    very excited!!!!

  • @4th_Dimension_I2b
    @4th_Dimension_I2b 3 ปีที่แล้ว

    Sal Sir can really make us learn anything.

  • @katunduchabala7266
    @katunduchabala7266 ปีที่แล้ว

    Super cool video! Thanks!

  • @ronaldoggha1801
    @ronaldoggha1801 2 ปีที่แล้ว

    what an excellent explanation. Thank you so much

  • @LiftingShark
    @LiftingShark 2 ปีที่แล้ว

    I am very very excited indeed

  • @justinwhitening4828
    @justinwhitening4828 3 หลายเดือนก่อน

    thank you for your help!

  • @SträvenA-n7v
    @SträvenA-n7v หลายเดือนก่อน

    I love you Khan Academy!

  • @zalanszabo4382
    @zalanszabo4382 ปีที่แล้ว +2

    Im edging to this guys voice

  • @collegeupdates2354
    @collegeupdates2354 4 ปีที่แล้ว

    Easiest explanation of derivative and not at all boring .

  • @danielwalker2381
    @danielwalker2381 5 ปีที่แล้ว +6

    Visually looking at derivatives doesn't make sense but numerically it makes more sense...idk why...I think it's because you think "oh, x^2 is continually changing more and more and more, so how could the derivative be a line 2x?" oof lol

  • @rodolfo5651
    @rodolfo5651 2 หลายเดือนก่อน

    i was preparimg for a good nap as you ended the videp. I need to develop self control😤

  • @ruixue6955
    @ruixue6955 4 ปีที่แล้ว +1

    0:36 delta is shorthand for change

  • @julianbastian6723
    @julianbastian6723 3 ปีที่แล้ว +1

    our teachers teaches us what to press in the calculator to solve the problems not derivatives

  • @chivasluis1
    @chivasluis1 3 ปีที่แล้ว

    That was intense. A very good intense.

  • @shahreenchowdhury1086
    @shahreenchowdhury1086 5 ปีที่แล้ว

    Now the organic chemistry tutor channel is good for working out a specific concept but khan academy is good for explaining cocepts.Thanks for th video it was,😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍

  • @much_tunsia
    @much_tunsia ปีที่แล้ว

    this was just so good

  • @chillout-gamezextreme
    @chillout-gamezextreme 5 หลายเดือนก่อน +1

    2:10 Avarage rate of change 🎉

  • @AwabWahib4
    @AwabWahib4 2 หลายเดือนก่อน

    Thanks a lot❤

  • @ryannatuor344
    @ryannatuor344 3 ปีที่แล้ว

    I've been learning derivatives in highschool for almost two years and only now I realise what the derivative actually is

  • @florentinosanchez3969
    @florentinosanchez3969 3 ปีที่แล้ว

    I finally get it, thank you

  • @mhm8742
    @mhm8742 2 ปีที่แล้ว

    this was sooooo helpful tysmmm

  • @Lilesme135
    @Lilesme135 7 ปีที่แล้ว +29

    You're voice would be really good to narrate creepypastas.

  • @spiderman10101
    @spiderman10101 3 ปีที่แล้ว +1

    Well explained