# 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 Universe9 months 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 borate9 months agoIt’s the Aretha Franklin formula!

toonsee9 months agoWas this a tribute to Aretha Franklin? Regardless, I love it! Thank you! #chainchainchainchainoffools

pikkupoika latexipuvussa9 months agoDamn seriously I suck at calc and I solved this almost immediately after seeing the integral

ארד ארבל9 months agoYou really HAVE to make a calendar with this problems of this kind for every day lol

etotheipi9 months ago^{+3}Just letting you know, the title says that this is a HMMT November problem but the problem is HMMT February.

Great video!

LetsSolveMathProblems9 months ago^{+1}Oops! You are absolutely right. I just fixed the title. Thank you so much for notifying me! =)

M Rizvi9 months agothis was not that kind of integral to baffle seasoned practioners

Ara9 months agoThis is like a nested function.just a nice trick.....👍👍😃😃

Snejpu9 months ago^{+2}It would be pretty easy if the first term was cos(sin(sin(sinx)))). Then f(x)=sin(sin(sin(sinx)))).

HARRIS LAM9 months ago^{+3}This one's cool!

cagsh xjusus9 months ago^{+21}This is the easiest one you've done in a while.

Sedeanimugamez9 months 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 Nikhil9 months agoOr even so complicated that you don't even feel like looking at it after reading it once.

HelloItsMe9 months agoOnly easy if you know the secret. Otherwise it can be quite hard

Novasix39 months 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

Kyro9 months 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

LetsSolveMathProblems9 months 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.

δτ9 months 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 savage9 months ago^{+12}Me: god please send me a sign!!

God:

Mihai Ciorobitca9 months agoJoshua Ong negative cosign ;)))

Joshua Ong9 months ago^{+1}tom God: sends cosign

Hannah Winter9 months ago^{+24}This is one of those "too good to be true" problems.