Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007

[NganaJHone]

I am very happy to see the vidoe from you, hopefully the others also are happy for You Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007

[Ondelendo]

Steady I Really Like This Video Chain rule Higher derivatives

[bebeheuy]

Good, I like that you share this video, I wish success always Chain rule Higher derivatives

[willamricard]

Nice Video That You Share , So Very Nice Thanks You Chain rule

[imegatrone]

I Really Like The Video From Your Chain rule Higher derivatives

[bundawartini]

Your Video Is Very Useful Sharing Chain rule Higher derivatives

[anakmudajaman]

after i watched this video Chain rule Higher derivatives, my insight is very open because the video is very good to give information

[keithl28]

Cool video

[swampscottsoccer]

7 people took statistics

[agapitoflores001]

Awesome. If I were to evaluate, I'll rate it more than excellent.

[prantare]

Can someone explain to me why delta v -> 0 as delta x -> 0? :)

[othitito]

@prantare Because delta v represents the change of the value of v from the original v(x) value (in other words, delta v = "new" v - "old" v). As delta x goes to zero, "new" v and "old" v become the same (if v is continuous at this "old" v value, by the definition of continuity), and therefore the delta v approaches zero. Make sense?

[thePENANCE]

I wonder what happened to students on their exams when they went in not knowing the correction for u, because they were told it was for x haha.

[LAnonHubbard]

@thePENANCE ha ha :)

[cberns223]

Im trying to break my slacker lifestyle, and go back to school for Chem E and this is definitely making me excited.

[barca17]

why do they laugh at the chain?

[jeebedon]

@barca17 "Is it because it chains you down?" asks Dr. Miller. Of course, very mature college students laugh at the secual innuendo behind it.

[MegaPukpui]

I think the derivative of U(x)V(x) ,we should add and substract u(x+deltax).v(x) instead of u(x) .....

[wrzazq]

@MegaPukpui No. It will work for the proof because when lim x->0 the proof is correct. So for derivatives, it's fine if you write that way, but otherwise the mathematical proof is wrong as it won't equate for limits other than 0.

If I'm not clear enough, you are dropping a u.deltax in the proof from thin air. Remember whatever change you make to the formula, it must equate the previous formula, and it will only equate when u.deltax = 0, that is, when lim x->0.

[MegaPukpui]

I think the derivative of U(x)V(x) ,we should add and substract u(x+deltax).v(x) instead of u(x) .....

[SF1010]

The chain was awesome lol

[behnamasid]

He actually brought a chain, lol

[manrajabi]

thank you mit, supposing i am going to donate , how can i do this from iran?

[caroleabumoussa]

LOL... I just wanna burst free from math!!! :P

[Darkkaz118]

29:10 I want to break free!

[adidasguy87]

the higher derivative section seemed to be kind of a waste of time besides that i thought he did good

[respaldoqtz]

Que se supone que está explicando..???? está demostrando saltándose pasos de álgebra como si por eso fuera a ser mejor demostración... que quiere demostrar... que sabe y que es chingón... a los estudiantes hay que poner cada paso y exponer con claridad, nadie puede asimilar eso en una clase... PÉSIMA EXPLICACIÓN

[Jameswb98]

@respaldoqtz No encontre los saltos demasiado largos ni los pasos dificiles a seguir. Hay que acordarse de que la audencia intendida son estudiantes ya bastante conocidos en los metodos algebragicas.

[respaldoqtz]

@Jameswb98 Lastima por tí... ¿hay que recordar? se recuerda lo que se conoce y despues se olvida, a mi nunca se me informo de la capaciodad de la audiencia así que no tengo que recordar nada sobre ellos... los "metodos algebraicas" como lo escribes, creo que sé a que te refieres y no son garntía de demostración si no se profundiza en la justificación de cada acción algebraica, si no se hace esto se pueden cometer falacias muy bien disfrazadas

[yoyaya007]

MIT is the best. thank you MIT !!!

[lucasas8]

Liked that teacher! he is funny ^^

great class \o

[yyttr4]

I love this guy, he actually shows the FULL way to do things. And his proof for the product rule is beutiful <3

[goel1992]

Thank You MIT really appreciate what you doing.

[LogicalFlawDetector]

This guy is a substitute. He sucks. Professor Jerison is better (Prof. Mattuck is the best!). I had to look at the printed out notes from the M.I.T OCW website that I have to make sense of what he said. This has never happened with Jerison.

[bjim217]

The chain rule proof is incomplete without a proof about the limit of products being equal to the product of the limits.

[Antoniocastagnoli]

I think the regular professor is better! Well, I liked the way he taught the chain rule, but I didn't like the way he proved the product rule and the quocient rule.

[caramonspace]

The Chain Rule: it lets you burst free!

[tobuslieven]

This guy's great : ) thanks mit

[zamaxx]

This is helping me a lot, I think that's the way mathematics must be explained. I understand it better than in my native language...

Thks

I WOULD LIKE A COMPLETE COURSE OF PHYSICS, THAT WOULD BE GREAT...

[jogaserbia]

@zamaxx

MIT has one. 18.01 is the physics 1 videos. I believe there is also 18.02 and 18.03

[sonisucks]

shaikfiaz, think about this. a is changing a some rate and b is changing at some rate. now you want to know how a is changing relative to b.... this might be confusing at first but think about this might help: say you have a car with velocity A, and another car with velocity B. by using the the this rule, you can determine the velocity of A relative to the velocity of B, or if you want, the other way around.... someone want to make shore im rite on this though...

[henock11]

hes "the substitute", but i sure liked how he explained that chain rule! very helpful.

[adam3141]

This is great. I never got to learn this stuff in college so it is great to actually learn this at home in my own time which is video after video after video... Accelerated learning is great.

[shaikfiaz]

Can some one give me the explanation: why (dy/dt)=(dy/dx)(dx/dt)? I can see the simple algebra but of cancellation but how is it true in terms of change in x and t.

[wheelygood9]

Thanks for this MIT - a great aid for me.

[michalchik]

Thanks again to the people who put this up. I liked this guy even better though the regular guy is good.

[felix10271]

I've just noticed that my teacher never taught me the entire steps...just the short cuts. This is great!

[gph404]

@felix10271 your teacher probably didn't know the actuall proof or derivation herself.  HS teachers are often dumb anyway

[achrispens]

This guy is awesome! Thanks to all who uploaded all these videos for the public . YOU ALL ARE THE BEST!

I noticed fewer comments and much fewer number of views as the videos progress. Clearly, this is not for the weak. All of these mathematics videos are fantastic. Please try to upload an undergraduate Abstract Algebra video soon. I could really use a good review.

[honeybbqgrundle]

Ok, youtube is ridiculous with links. Let's try this

h t t p : / / w w w . u c c s . e d u / ~ m a t h / v i d a r c h i v e . h t m l

You have to sign up, but it's free and they have abstract algebra lectures.

[achrispens]

Thanks sooooo much for the link. The professor is fantastic.

[keyblade134679]

hey um..., for some reason i cant watch any of the video in the web site you posted here. Whenever i click on the video icon it just loads but never get there.

[zamaxx]

That's because you don't have the plu-in necessary for seeing the video like a flash player or a quick time player and so...

[petersodgmailcom]

I should have mentioned that the d's are pronounced Dee:

lo dee hi minus hi dee lo square the bottom and off you go.

[petersodgmailcom]

I learned a simple "poem" to remember the quotient rule:

the derivative of hi/lo (numerator = hi, denominator = lo) is equal to:

lo d(hi) minus h d(lo) square the bottom and off you go.

1971 calc class!

[felix10271]

AGGH Brilliant. My Calc teacher forgot the last part. Now I can make the whole thing rhyme!

[hyperzzip]

Great lecture. Thank you very much!