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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[@fluffyrawan7656]

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

[@AaBb-qs6gh]

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]

couldn't agree more!

[@unknownunknowns]

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

[@Devilfish4387]

true and sad

[@kgtech6882]

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

[@digit975]

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]

I agree.

[@luxfries1524]

Learn trigonometry

[@luxfries1524]

Nvm this was 3 years ago

[@fraddi]

CALCULUS WAS INVENTED IN INDIA. THE EUROPEANS STOLE IT.

[@alkazi1482]

@@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.

[@superawesomecaptainmcfluff9506]

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]

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

[@resurgam2243]

@@r.s.banimations561 In most schools.

[@viveksukhla8631]

@@r.s.banimations561 in every school

[@parulaggarwal9405]

👌👌

[@aarohansharma4551]

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]

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]

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

[@theopenacademy9102]

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]

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]

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.

[@zoombae]

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

[@ankitaaarya]

Yes if you're not joking

[@adamrosstoledobriones8881]

yes

[@SamitaSarkar]

His voice is great

[@adiliraliyev5882]

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

[@arogueburrito]

nah I don't think so

[@randyshi72]

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

[@uniqueh5203]

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 !

[@ameesinghamazing3825]

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!"

[@joedimon]

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.

[@swarajrajpure8073]

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

[@fraddi]

CALCULUS WAS INVENTED IN INDIA. THE EUROPEANS STOLE IT.

[@kartikeyekhanna2657]

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

[@ellastevens5638]

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!

[@paulaan881]

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

[@MichiganPeatMoss]

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

[@E7R1I6C]

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

[@ValidatingUsername]

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.

[@jadesanjose2520]

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... :)

[@tthproductions8076]

Im using khanacademy rght now :)

[@nickh.44]

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

[@princessEA7]

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

[@alessandromalfa3919]

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

[@MeinCouch123]

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.

[@yummytacos3357]

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

[@quriositysquared1028]

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

[@fatimah.tulkubra2447]

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

[@frankenstein3397]

this explanation clears my dy/dx doubt,thanks.

[@RicardoMartinez-jy5lo]

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.

[@Jesse_The_Lazy]

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

[@Kate-zz4nk]

You explained this extremely well! It actually makes sense now

[@asparagus7014]

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

[@rajib05555]

Excellent video thanks a lot!!

[@caratinawaiters2590]

Your excitement in this video is breathtaking

[@Albeit_Jordan]

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]

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]

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

[@ExplainIttoMe_1]

@@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]

@@reginaphilange6478 Derivative is the "slope" at x

[@benv5115]

You're a national hero!

[@krishnaca65]

very nicely explained sir.

[@WhovianRanger42]

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

[@proudamazighian9334]

The first and already the best math channel I found

[@hotball5361]

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

[@michio028yt8]

thaks you you teached me enought to continue learning

[@johnnamtae9610]

Your handwriting is so good in these.

[@LeonardoDelCarpioBellidoVargas]

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

[@millenial1986]

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

[@TahiraZubair-t3o]

My favorite course 😊

[@danielwalker2381]

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

[@abhyudayaaware8653]

very excited!!!!

[@MGTMusic]

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

[@vadrif-draco]

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

[@conradkotze4615]

This makes so much more sense!

[@julianbastian6723]

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

[@soleunderdeepsea6585]

Then you should do it😄

[@julianbastian6723]

@@soleunderdeepsea6585 sure i already do and im only 14

[@melsitler]

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!

[@b-lifestyle7263]

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!

[@phatphan1403]

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

[@khalilgueye5097]

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

[@diegoespinoza8997]

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.

[@haydenhartmann2034]

I am very very excited indeed

[@ronaldoggha1801]

what an excellent explanation. Thank you so much

[@gouisedeau]

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

[@katunduchabala7266]

Super cool video! Thanks!

[@vatsayana2004]

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

[@DylanWoods-kw6km]

I'm in 7th grade teaching my self calculus KZbin is the best

[@ЮлияШтундюк]

Finally got it, thank you for insight!

[@justinkim7202]

Loving these lessons!

[@pranavp.a1200]

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

[@pranavp.a1200]

Lakshaydeep thank you

[@collegeupdates2354]

Easiest explanation of derivative and not at all boring .

[@much_tunsia]

this was just so good

[@bibauu]

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

[@chivasluis1]

That was intense. A very good intense.

[@mhm8742]

this was sooooo helpful tysmmm

[@thewisearchitect]

You are so good!

[@fataldreidel5846]

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]

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.

[@shahreenchowdhury1086]

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

[@user-hc9dk2dl9i]

this helps so much

[@florentinosanchez3969]

I finally get it, thank you

[@ammarchen8850]

Thank you so much khan academy

[@zalanszabo4382]

Im edging to this guys voice

[@abdikhaliqaden5731]

Calm tf down

[@allywilliams6849]

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

[@tuannguyenhoang8735]

Thanks so much

[@Arandomguyat1]

brilliantly explained as usual

[@Lilesme135]

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

[@dhurbarajpuree2992]

Great teacher u are

[@drmalpractical]

Thank you

[@sebastianr3460]

I hadn´t understood the concept of rate of change until this video.

[@jaydencole-yq2vp]

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.

[@jessye2325]

Thank you !

[@dakshgiri3367]

Awesome!

[@ruixue6955]

0:36 delta is shorthand for change

[@nikulbhati7733]

thanks

[@paterfamiliasgeminusiv4623]

Great, great, this is good :)

[@pereirao]

Excelent explanation!

[@molefiledwaba5245]

Which software are u using to teach here. Looks great

[@hunterterrell9930]

Speed is defined as distance/time, if time is 0 then distance is also 0, without time, there is no motion, and without motion, there cannot be speed. I think.

[@Silver_Channel98]

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

[@duaafatima-nk3bo]

NICE

[@ryannatuor344]

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

[@konozrashid887]

Just like you showed the proof of the derivatives of different functions, do you also have videos which show the proof of integration of differentiation functions? If so, please give me the link of those videos.

[@kashkid7777]

math is hard

[@rootuser5143]

Hey the tangent has some y intercept what does that mean ? Before we started to account time there was some distance travelled or in negative time some distance was travelled And one more thing for the same tangent the slope dy/dx The distance travelled Or the time taken to travel a distance will be dy/dx=(y-its intercept)/x Some one please comment if my thinking is correct

[@azatfree]

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)