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"

[@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.

[@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!!

[@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!"

[@randyshi72]

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

[@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

[@kartikeyekhanna2657]

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

[@joedimon2645]

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.

[@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!

[@gouisedeau]

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

[@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.

[@MichiganPeatMoss]

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

[@quriositysquared1028]

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

[@Tom-sq2nt]

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

[@Kate-zz4nk]

You explained this extremely well! It actually makes sense now

[@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... :)

[@mohamedaminebaccar8095]

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

[@LoganSnyder]

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]

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

[@LoganSnyder]

@@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]

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

[@vadrif-draco]

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

[@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

[@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

[@Shivshankar_JEE-ov5wx]

Sal Sir can really make us learn anything.

[@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.

[@tthproductions8076]

Im using khanacademy rght now :)

[@paulaan881]

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

[@frankenstein3397]

this explanation clears my dy/dx doubt,thanks.

[@user-hc9dk2dl9i]

this helps so much

[@hotball5361]

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

[@rajnish8918]

brilliantly explained as usual

[@user-wy1js8tc1z]

Finally got it, thank you for insight!

[@ronaldoggha1801]

what an excellent explanation. Thank you so much

[@jessetrammell5678]

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

[@pereirao]

Excelent explanation!

[@conradkotze4615]

This makes so much more sense!

[@proudamazighian9334]

The first and already the best math channel I found

[@caratinawaiters2590]

Your excitement in this video is breathtaking

[@princessEA7]

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

[@johnnamtae9610]

Your handwriting is so good in these.

[@justinkim7202]

Loving these lessons!

[@rajib05555]

Excellent video thanks a lot!!

[@michio028yt8]

thaks you you teached me enought to continue learning

[@katunduchabala7266]

Super cool video! Thanks!

[@asparagus7014]

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

[@WhovianRanger42]

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

[@amangarg3858]

This is what I exactly looking for😀😀😀

[@chivasluis1]

That was intense. A very good intense.

[@user-fp5bz2ux2p]

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

[@florentinosanchez3969]

I finally get it, thank you

[@paterfamiliasgeminusiv4623]

Great, great, this is good :)

[@maskedmarvyl4774]

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.

[@megancower1884]

Wow. I feel things are about to click.

[@mhm8742]

this was sooooo helpful tysmmm

[@MGTMusic]

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

[@much_tunsia]

this was just so good

[@phatphan1403]

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

[@ammarchen8850]

Thank you so much khan academy

[@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,😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍

[@krishnaca65]

very nicely explained sir.

[@dhurbarajpuree2992]

Great teacher u are

[@abhyudayaaware8653]

very excited!!!!

[@collegeupdates2354]

Easiest explanation of derivative and not at all boring .

[@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.

[@haydenhartmann2034]

I am very very excited indeed

[@ivanasintic8543]

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

[@sebastianr3460]

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

[@jessye2325]

Thank you !

[@bibauu]

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

[@spiderman10101]

Well explained

[@blkcat17]

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!

[@khalilgueye5097]

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

[@thewisearchitect]

You are so good!

[@nikulbhati7733]

thanks

[@benv5115]

You're a national hero!

[@ryannatuor344]

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

[@tuannguyenhoang8735]

Thanks so much

[@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

[@dakshgiri3367]

Awesome!

[@vatsayana2004]

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

[@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.

[@pranavp.a1200]

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

[@pranavp.a1200]

Lakshaydeep thank you

[@SchwanaCARDHUT]

Bravo 👏👏 et Merci ..................

[@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.

[@meloniejen8400]

Amount of likes is the amount of lives Khan has saved

[@drmalpractical]

Thank you

[@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

[@NotWhatYouThinkSom]

Thank you Khan academy

[@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.

[@etoileepanoui6011]

I was having a breakdown because I literally couldn’t understand it due to the way my teacher was explaining it. Thank you, so, so much.

[@DylanWoods-kw6km]

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

[@ther7554]

If my teacher would have taught me in this manner i would never have wasted time in gaming anymore...this thing itself a very interesting game🤗

[@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

[@ruixue6955]

0:36 delta is shorthand for change

[@hamedhasan5843]

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"

[@josephajoseph9535]

Give this man a manhatten project!❤

[@40fpskiller]

Awesome