# Harvard-MIT: Chain-Chain-Chain Rule (2009 Feb #2)

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- Published on Sep 3, 2018
- Let's quickly make sure we know how to apply chain rule multiple times.

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Quahntasy - Animating UniverseYear ago^{+1}This is the easiest one you've done in a while.

Is it possible if you can do a whole test and stream it or something? It would be interesting.

L borateYear agoIt’s the Aretha Franklin formula!

toonseeYear agoWas this a tribute to Aretha Franklin? Regardless, I love it! Thank you! #chainchainchainchainoffools

pikkupoika latexipuvussaYear agoDamn seriously I suck at calc and I solved this almost immediately after seeing the integral

ארד ארבלYear agoYou really HAVE to make a calendar with this problems of this kind for every day lol

etotheipiYear ago^{+3}Just letting you know, the title says that this is a HMMT November problem but the problem is HMMT February.

Great video!

LetsSolveMathProblemsYear ago^{+1}Oops! You are absolutely right. I just fixed the title. Thank you so much for notifying me! =)

M RizviYear agothis was not that kind of integral to baffle seasoned practioners

selraYear agoThis is like a nested function.just a nice trick.....👍👍😃😃

SnejpuYear ago^{+2}It would be pretty easy if the first term was cos(sin(sin(sinx)))). Then f(x)=sin(sin(sin(sinx)))).

HARRIS LAMYear ago^{+3}This one's cool!

cagsh bghhcvvYear ago^{+21}This is the easiest one you've done in a while.

SedeanimugamezYear agowhat secret if you finished calculus heck even calculus ab this shouldn't be any hard its logic using the fundamental theorem of calculus and chain rule, novel concepts there are really scary problems much scarier than this.

Sai NikhilYear agoOr even so complicated that you don't even feel like looking at it after reading it once.

HelloItsMeYear agoOnly easy if you know the secret. Otherwise it can be quite hard

Novasix3Year ago^{+26}Would it be possible for you to take a whole test like this, and show it to us ? I think it could be very interesting to see the whole reasoning behind the big test, if you have time/motivation of course

KyroYear ago^{+7}I think it's much easier to just think of the problem as a first order differential equation, integrate both sides with u-sub, and solve for C

LetsSolveMathProblemsYear ago^{+3}You may be right. I actually considered presenting the solution using u-substitution, but I decided that may be an unnecessary extra step for this particular problem, whose solution is quite easy to guess. However, some viewers may prefer the solution using substitution.

δτYear ago^{+3}That is essentially exactly what he has done here, with sin(sin(sin(x))) = u and thus du = cos(sin(sin))*cos(sin(x))*cos(x) dx .

He merely skipped the part of pointing out what u and du are and jumped forward to the primitive as it was sort of obvious, provided knowledge of the chain rule.

21 savageYear ago^{+12}Me: god please send me a sign!!

God:

Mihai CiorobitcaYear agoJoshua Ong negative cosign ;)))

Joshua OngYear ago^{+1}tom God: sends cosign

Hannah WinterYear ago^{+24}This is one of those "too good to be true" problems.