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

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Why we study differential calculus. Created by Sal Khan.
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AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
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Опубликовано:

29 сен 2024

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Комментарии : 326

@fluffyrawan7656 6 лет назад

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

@AaBb-qs6gh 4 года назад

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 4 года назад

couldn't agree more!

@unknownunknowns 4 года назад

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

@Devilfish4387 3 года назад

true and sad

@kgtech6882 3 года назад

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

@kartikeyekhanna2657 7 лет назад

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

@edgarcastro7227 7 лет назад

Hey sorry i need help for a college admission test what could You recommend me to study, would apreciate your help

@أَحْسَنُ.الْحَدِيْثْ 3 года назад

So what are u studying or what have u finished studying? 🤪😂😂😂I am a litte early to the party I guess😌😝

@zoombae 7 лет назад

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

@ankitaaarya 5 лет назад

Yes if you're not joking

@adamrosstoledobriones8881 4 года назад

yes

@SamitaSarkar 4 года назад

His voice is great

@adiliraliyev5882 4 года назад

Maybe you just feel like that towards people who teach you stuff?

@arogueburrito 3 года назад

nah I don't think so

@superawesomecaptainmcfluff9506 7 лет назад

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 6 лет назад

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

@resurgam2243 6 лет назад

@@r.s.banimations561 In most schools.

@viveksukhla8631 5 лет назад

@@r.s.banimations561 in every school

@parulaggarwal9405 5 лет назад

👌👌

@aarohansharma4551 5 лет назад

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!

@omniscienceisdead8837 3 года назад

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 Год назад

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

@digit975 7 лет назад

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 7 лет назад

I agree.

@luxfries1524 3 года назад

Learn trigonometry

@luxfries1524 3 года назад

Nvm this was 3 years ago

@fraddi 2 года назад

CALCULUS WAS INVENTED IN INDIA. THE EUROPEANS STOLE IT.

@alkazi1482 2 года назад

@@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.

@theopenacademy9102 6 лет назад

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!!

@ceejay1684 3 года назад

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 5 месяцев назад

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.

@E7R1I6C 3 года назад

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

@gouisedeau 5 лет назад

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

@randyshi72 2 года назад

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

@Albeit_Jordan 6 лет назад

I get confused at almost every use of the terms 'function' and 'derivative' as I thought they were synonymous... What am I misunderstanding? By extension, I'm not sure I understand f' (f-prime), either. Could someone help?

@ExplainIttoMe_1 6 лет назад

Albeit_Jordan A function is a relationship between one or more variables. For example, f(x) = x+3. A derivative is the instantaneous rate of change of the function at a point. Another way to think of a derivative is the slope of the tangent line at a point of the function. The f-prime notation is just another way to represent the derivative of a function. Hope that helps!

@reginaphilange6478 4 года назад

@@ExplainIttoMe_1 I'm so confused, so the derivative is the *y* of x??

@ExplainIttoMe_1 4 года назад

@@reginaphilange6478 The derivative represents the slope or rate of change of the function at one point. It is represented by f’(x), dy/dx, or y’. The function itself is usually represented by f(x) or y (without the apostrophe, which is read as “prime”).

@danielcervantes7826 3 года назад

@@reginaphilange6478 Derivative is the "slope" at x

@swarajrajpure8073 7 лет назад

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

@fraddi 2 года назад

CALCULUS WAS INVENTED IN INDIA. THE EUROPEANS STOLE IT.

@danielwalker2381 5 лет назад

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

@uniqueh5203 4 года назад

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 !

@ellastevens5638 Год назад

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!

@tthproductions8076 7 лет назад

Im using khanacademy rght now :)

@meloniejen8400 5 лет назад

Amount of likes is the amount of lives Khan has saved

@jadesanjose2520 4 года назад

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... :)

@mohamedaminebaccar8095 2 года назад

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

@Tom-sq2nt Год назад

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

@joedimon 3 года назад

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.

@kashkid7777 3 года назад

math is hard

@ameesinghamazing3825 Год назад

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!"

@LoganSnyder 4 года назад

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 4 года назад

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

@LoganSnyder 4 года назад

@@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 4 года назад

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

@maskedmarvyl4774 Год назад

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.

@paulaan881 3 года назад

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

@megancower1884 6 лет назад

Wow. I feel things are about to click.

@Lilesme135 7 лет назад

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

@sterlingsun3850 5 лет назад

thats my csgo crosshair lol

@asparagus7014 7 месяцев назад

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

@quriositysquared1028 7 лет назад

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

@pranavp.a1200 7 лет назад

can you please make a video on orbitals.electro negativity and related topics please...thank you

@pranavp.a1200 7 лет назад

Lakshaydeep thank you

@ValidatingUsername 4 месяца назад

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.

@vitalorgans4944 5 лет назад

I can’t believe I am in Gr. 5 and learning precalculus on my spare time 🤦🏻‍♂️

@jonas-ke4qz 5 лет назад

Potato City! good work!

@ericarizaazules 5 лет назад

Yeah right..

@funwithaiman 4 года назад

That’s awesome! It’s a brilliant idea and you’re making well use of your spare time. Knowing this beforehand will be highly beneficial. 😊

@gregoriousmaths266 4 года назад

Why the facepalm? I’m guessing that now you have moved on to higher maths such as category theory, topology, analysis etc. Either way that’s very impressive!!

@rajdeepsindhu9268 4 года назад

@@gregoriousmaths266 He's just looking for attention, in my humble opinion. If what he claims was really true, he would most probably not have mentioned it.

@julianbastian6723 3 года назад

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

@soleunderdeepsea6585 3 года назад

Then you should do it😄

@julianbastian6723 3 года назад

@@soleunderdeepsea6585 sure i already do and im only 14

@Jesse_The_Lazy Год назад

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

@alessandromalfa3919 2 года назад

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

@Noitisnt-ns7mo 2 года назад

Math, ultimately is rational lies. So sayith I.

@sebastianbalbo1906 Год назад

Aryabattha BRAHMAGUPTA BASHKARA SECOND manjula NOT LEIBNIZ NOT NEWTON

@anmolrattansinghsidhu1938 4 дня назад

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

@MichiganPeatMoss 2 года назад

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

@frankenstein3397 3 года назад

this explanation clears my dy/dx doubt,thanks.

@b-lifestyle7263 19 дней назад

Thanks for your video. I have a question with the rate of change equation. Why that's delta Y/ delta X ? what if delta X/delta Y for instead? Hope you can answer! Thanks again!

@the_infinity_snake 3 месяца назад

OVERALL, this video is pretty impressive, it is mostly understandable, but this 2:47 is very confusing because if it's the exact same point, then there's obviously no change at all, it's bad wording. 🙃

@princessEA7 5 месяцев назад

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

@chillout-gamezextreme Месяц назад

2:10 Avarage rate of change 🎉

@nickh.44 13 дней назад

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

@Clowddy Год назад

This was helpful, however I was looking for a Kingdom Hearts music video, I couldnt really get down with any of the beats in this and there wasn't any bASE drops or anything. not like that cool kingdom hearts music video. thank you for the knowldege though!

@Daniel__g12 2 месяца назад

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@Silver_Channel98 2 месяца назад

I'm confused about change in x and change in y. Why is that different from looking at a normal slope?

@azatfree Год назад

i do not understand why only dx approaches zero and dy doesnt. and if dx approaches zero doesnt it mean that dy/dx = 0 in any case? then what is the point of derivative of the point if it always approaches zero? (sorry for my broken eng)

@Kenneth-v2Kenneth___3q 2 месяца назад

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@RicardoMartinez-jy5lo 2 года назад

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.

@Enough736 Год назад

Same title as the review of my autobiographical one-man show.

@zalanszabo4382 10 месяцев назад

Im edging to this guys voice

@abdikhaliqaden5731 10 месяцев назад

Calm tf down

@studyaccount017 День назад

i'm not that down bad but real

@johnnamtae9610 4 года назад

Your handwriting is so good in these.

@roy020780 7 лет назад

what is the software you use to make presentation?

@pataliah 4 года назад

Camtasia or Snagit probably.

@nemehalotaibi 11 месяцев назад

so can we calculate the derivative of a line? wouldnt be just the slope itself or zero? i dont understand help lol

@niyonezabernard6045 2 месяца назад

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

@jaydencole-yq2vp Год назад

Hello khan academy pls i need your help on this question A vessel contains at 1 bar and 20°C a mixture of 1 mole of CO2 and 4 moles of air. Calculate for the mixture: (i) The masses of CO2, O2 and N2, and the total mass; (ii) The percentage carbon content by mass; (iii) The apparent molecular weight and the gas constant for the mixture; (iv) The specific volume of the mixture. The volumetric analysis of air can be taken as 21% oxygen and 79% nitrogen.

@Kate-zz4nk 2 года назад

You explained this extremely well! It actually makes sense now

@diegoespinoza8997 Год назад

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.

@johnpro2847 6 месяцев назад

who calculated the Usain Bolt speed graph

@yummytacos3357 13 дней назад

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

@shannonlenker1202 Год назад

this guys voice has a tonal quality that really makes me just not wanna listen to him

@vatsayana2004 2 года назад

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

@Siopc 7 месяцев назад

Bro's got the call of duty crosshair as a mouse icon :D

@melsitler 11 месяцев назад

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!

@nancymwewa9009 2 года назад

I am thinking about my Caucasian boyfriend Anthony in slope class....please God help 🙏

@essence-of-everything 4 года назад

Hi! I need a program por pc so that I can make presentations for Metallugy classses. So what program did you use in this video please? Thanks.

@viky1354 4 года назад

magnifier on ms paint i think

@pataliah 4 года назад

Camtasia or Snagit probably.

@millenial1986 10 месяцев назад

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

@hamedhasan5843 2 года назад

I'm half done with my college differentiation course and solved many problem without knowing what am I actually doing...then here I heard the phrase "instantaneous rate of change"

@molefiledwaba5245 11 месяцев назад

Which software are u using to teach here. Looks great

@visano. 6 месяцев назад

So basically, differentiation deals with tangent of a curve, and integration deals with the area under a curve.

@nguyentanphat2068 Год назад

Excuse me, can I ask you, is the derivative with respect to constant defined, if so, what is the derivative of 2x + 1 with respect to the constant 1?

@ravimanju7294 7 лет назад

no where better than this

@aufiyusrina5589 7 лет назад

can anyone tell me what app do they use?

@sberry-milk 3 года назад

I learned calc over ZOOM academy so safe to say I only really understood 70 percent and now I need to know it for my physics class and I didn’t even know what a derivative was calculating :/

@agathaporter3685 13 дней назад

Williams Sarah Gonzalez Donald Wilson Gary

@allywilliams6849 Год назад

I’m not even taking pre cal as a senior until next semester, but I’m in AP physics (algebra based), so it might help

@WhovianRanger42 9 месяцев назад

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

@MeinCouch123 2 года назад

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.

@DylanWoods-kw6km 7 месяцев назад

I'm in 7th grade teaching my self calculus RU-vid is the best

@zehn9614 7 лет назад

YEET

@zehn9614 7 лет назад

oh yeah first baby

@bengalurudiaries1523 6 лет назад

Isn't the term "Instantaneous Change" an oxymoron? Change happens over a time, not in a single instance, so what does Instantaneous change exactly mean?

@tharun7290 5 лет назад

You know, its more of an abstarct term than a solid fact kinda term

@stewpeed6327 5 лет назад

it means a change of an instant, thus instantaneous change, not a change that happens instantly

@fatimah.tulkubra2447 Месяц назад

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

@ham164cs 7 месяцев назад

Can someone explain what “prime” means when talking about “f prime”?

@Siopc 7 месяцев назад

im shite at maths but i think it's first derivative

@sirbuttertown6455 3 года назад

why does every single person say "instantenous rate of change" when describing derivatives. they say it like religion and never go in to context or anything.

@marciamarquene5753 Год назад

Só se for o almoço amanhã às noite toda hora

@Carrymejane 8 месяцев назад

This man sounds so sexy bruh, high and deep

@Theoceanismoist 3 года назад

I came here for an explanation for a meme. Thank you very much sir.

@shelumieldylen2621 2 года назад

how can there be any change in an instant?, wouldn't change just requires two specific points in time??

@drofeng Год назад

The average rate of change is between two points (e.g. DeltaY/DeltaX), but taking the limit as DeltaX approaches zero gives the instantaneous rate of change

@sj_rocks Год назад

Where to i go to start at the total beginning?

@hotball5361 2 года назад

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

@phatphan1403 3 года назад

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

@shahreenchowdhury1086 5 лет назад

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,😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍