No video :(

Product rule proof | Taking derivatives | Differential Calculus | Khan Academy

Подписаться 9 млн

Просмотров 169 тыс.

50% 1

Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacadem...
Watch the next lesson: www.khanacadem...
Missed the previous lesson?
www.khanacadem...
Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Differential Calculus channel:
/ channel
Subscribe to KhanAcademy: www.youtube.co...

Опубликовано:

14 авг 2024

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 75

@potrkca 7 лет назад

thank you - much better explanation than what i was looking at in my calculus course material.

@barryhughes9764 7 лет назад

What can I say....brilliant explanation of the product rule for derivatives.

@sarashowkat3676 3 года назад

@@zadocktoo3652 what?

@MohaMMaDiN55 5 лет назад

I knew that the only one who could explain this is the blessed Mr. Khan. without you, I wouldn’t have such knowledge in math and calculus

@Mohd-l 2 года назад

تخرجت ؟

@MohaMMaDiN55 2 года назад

@@Mohd-l اي :)

@Mohd-l 2 года назад

@@MohaMMaDiN55 تشتغل حاليا؟

@michaelajadedesousa3473 7 лет назад

Exceptional Mr Khan. You are appreciated in South Africa!

@implicit2656 7 лет назад

waarheid

@mcebisidube4248 6 лет назад

Second that 🙏

@Samuel-hw6in 3 года назад

I never fully understood this during my A-Levels 10 years ago, and had to just memorise the final formula. Now I get it!! Thank you so much :D

@TheSentientCloud 9 лет назад

One of the sexier proofs, IMO. :D

@Bhamilton-ws4go 5 лет назад

Definitely elegant

@trendypie5375 5 лет назад

i am gonna be a tutor like you Mr. khan . you are my inspiration

@holy_nuke8479 4 года назад

Great!!!!!!!

@drunknhamster4708 4 года назад

This also proves integration by parts just by doing a little bit more algebra

@PenandPaperScience 3 года назад

For those of you that want to practice some exercises, in my latest video I go through exactly these exercises step-by-step, explaining everything I do along the way. Perhaps it helps some of you :)

@idrissulaiman8865 Год назад

I really appreciate your effort mr khan

@23232323rdurian 5 лет назад

Excellent as always! U are a great teacher! May I humbly suggest: A transcript of the blackboard notes could be very useful. We copy out Ur blackboard longhand anyhow. Much simpler to just copy/paste a transcript... I imagine Ur digital blackboard already generates them.. Maybe it's already available but I just dont know it?

@cpotisch 4 года назад

Logarithmic differentiation is far more efficient here. I really think the chain rule should be taught much earlier. With just the sum and constant rules, the derivative of sine, and the derivative of ln, one can easily differentiate any function.

@Darieee 8 лет назад

Thanks a lot !

@udhaykumaar8582 Год назад

Firstly,... Brilliant explanation of the rule,helped me a lot but I still have a doubt about taking f(x+h) as f(x)

@justinpark939 5 лет назад

That was a very nice approach I learnt. Thank you.

@calebpresto8684 8 лет назад

Where did you get f(x+h)g(x) ? I get it cancels out, but where did that come from?

@JPGberg 8 лет назад

I really hope it was trial and error as I am unsettled by the thought that somebody could intuit that applying +f(x+h)g(x) -f(x+h)g(x) would allow you to derive the formula...

@onlygoodpartloop 5 месяцев назад

Whenever I teach this to anyone I will write at the end, - by Sal Khan

@JPGberg 8 лет назад

"If at any point you feel inspired, I encourage you to pause this video." Spoken while my finger was on the space bar. Great time to try and prove as the only thing that is not intuitive is that one first algebraic manipulation, which would seem totally arbitrary if we didn't know it was necessary to prove the product rule.

@HL-iw1du 7 лет назад

Is there a way to generalize the product rule, as in a rule considering the derivative of the product of three functions or more instead of just two?

@drmichaelsunsschoolformath 6 лет назад

Yes just apply the product rule twice

@smhaque31 Год назад

Thank you Sal for your nice explanation, my daughter loves your explanation 🙏🙏🙏

@user-rm2qj2jh4l 9 месяцев назад

Thank you!!! I love proofs like these so I don't just need to blindly trust that it works! :) Great content!

@johnsknows3135 Месяц назад

great thx!

@sleepykitten2168 Год назад

Smart!

@rickhoro Год назад

Beautiful! Thank you.

@protivamondal5112 2 года назад

Someone get this guy a drummer.

@rubic64 7 лет назад

wow, u have saved my a lot of times

@crimsonnn Год назад

why they never teach this in any calculus course?? like it's fundamental

@monthihan Год назад

amazing explanation. thank you.

@sarasneethu8277 4 года назад

Thank you so much, my Professor skipped so many steps😭

@SOBIESKI_freedom 9 лет назад

Why audio is so low?

@dirtyslim33 2 года назад

You are a lifesaver!!!!

@mohammadmaasir3270 3 года назад

Thnx for nice explaination...

@yeetntnt2903 4 года назад

this is a brilliant explanation! thank you

@alagiefatajo947 5 лет назад

wow! Masha allah , thank you mr.Khan

@dijkstra4678 2 года назад

6:25 he read my mind

@user-ye6sw5nk9k 10 месяцев назад

Excellent 👍

@sankhuz 3 года назад

Thx from india... Just another jee aspirant

@marylamb6063 Год назад

What gives you the "right" to factor out f (x+h) from the numerator? I understand why you can factor out g(x), since it has no h in it. But f(x+h) has h as a numerator. How do we justify removing the denominator from it?

@saunyboy123 9 лет назад

Easy way to remember product rule: Keep diff + diff keep

@HHHHHH-kj1dg 3 года назад

Very clever.

@jarrethcutestory 8 лет назад

Very well explained, well done

@donsena2013 Год назад

Well proven

@mo.G_2020 9 месяцев назад

So much easier than Wikipedia

@MaryashrafBaly 3 года назад

Fantastic ❤️✨

@qualquan Год назад

Easier if f(x+h) depicted as f(x)+df and g(x+h) as g(x)+dg Then THEIR product is simply: f(x).g(x) +f(x).dg +g(x).df +df.dg Then subtracting f(x).g(x) and dividing by dx gives: f(x).dg/dx +g(x).df/dx +df.dg/dx or f(x).g' + g(x).f' while the remaining term df.dg/dx is removed as it contains ALL the averaging error (not because it is zero) BTW, since f(x+h) is f(x) + df So f(x+h). g' = f(x).g' + df.g' Then df.g' is eliminated as it contains averaging error and NOT because it is zero.

@shybound7571 4 года назад

this is magic

@ahmedezzat687 2 года назад

Great

@choungyoungjae8271 3 года назад

perfect

@gamingguys6571 5 лет назад

Thanx bro

@Caradaoutradimensao 4 года назад

our Saviour!

@overlordprincekhan 3 года назад

Lol.. I get that what he mean now. Excellent explaination.

@emanuelradu4104 2 года назад

Thank you for the video but I think this proof is not correct because lim as h->0 of f(x+h) is Not equal to f(x). That is the same with saying that lim as x->a of f(x) = f(a) which is not true. That being the whole point of the limit, to show that the value that your are approaching is not the same with the value of the function at that point. Think of it like this: looking for the value that f(x+h) approaches when h->0 is the same with looking for the value that f(n) approaches when n->a (some random value a). The values that f(n) takes when is goes closer and closer to a are not neccesarly closer and closer to f(a). That's why there is a value for f(a) and another value for the limit. I hope it's not pure nonsense what I ve just wrote.

@iqbalm6407 7 лет назад

Audio ?????

@billyjiang8829 8 лет назад

This is one of the proof. So is there another proof that is also valid. I'm just curious

@timo86m 8 лет назад

Leibniz has one. Was so excited he wrote his mom about it. I like it and it's graphical using rectangles

@mevlanisufi2100 7 лет назад

please, sent any link or source we can find that

@oneinabillion654 6 лет назад

Who came here from MIT lecture? You know what I mean :'D

@kylesheng2365 4 года назад

@Rev limits shut up, it's just a joke

@kylesheng2365 4 года назад

@Rev limits ?

@holy_nuke8479 4 года назад

@Random Autonomous Drone Pilot Hi khan academy is great ofc we'd watch it . Also dont forget life savers like Sal in here is of Bangladeshi descent , so if you want pure american content go pay the fortune to get into harvard or something

@holy_nuke8479 4 года назад

@Random Autonomous Drone Pilot Good for you :) and who exactly are the "we" you're assuming me to be ?