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

Share
Embed
• Published on Sep 3, 2018
• Let's quickly make sure we know how to apply chain rule multiple times.
Your support is truly a huge encouragement.
Every subscriber and every like are wholeheartedly appreciated.

• 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 borate Year ago

It’s the Aretha Franklin formula!

• toonsee Year ago

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

• Damn seriously I suck at calc and I solved this almost immediately after seeing the integral

• ארד ארבל Year ago

You really HAVE to make a calendar with this problems of this kind for every day lol

• etotheipi Year ago +3

Just letting you know, the title says that this is a HMMT November problem but the problem is HMMT February.
Great video!

• LetsSolveMathProblems  Year ago +1

Oops! You are absolutely right. I just fixed the title. Thank you so much for notifying me! =)

• M Rizvi Year ago

this was not that kind of integral to baffle seasoned practioners

• selra Year ago

This is like a nested function.just a nice trick.....👍👍😃😃

• Snejpu Year ago +2

It would be pretty easy if the first term was cos(sin(sin(sinx)))). Then f(x)=sin(sin(sin(sinx)))).

• HARRIS LAM Year ago +3

This one's cool!

• cagsh bghhcvv Year ago +21

This is the easiest one you've done in a while.

• Sedeanimugamez Year ago

what 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 Nikhil Year ago

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

• HelloItsMe Year ago

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

• Novasix3 Year 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

• Kyro Year 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

• LetsSolveMathProblems  Year 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.

• δτ Year 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 savage Year ago +12

Me: god please send me a sign!!
God:

• Hannah Winter Year ago +24

This is one of those "too good to be true" problems.