Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem

MIT 18.100A Real Analysis, Fall 2020
Instructor: Dr. Casey Rodriguez

We begin proving key properties of derivatives, such as the infamous product rule, quotient rule, and chain rule. We also prove the Mean Value Theorem (MVT), the low-key hero of calculus, and consider some applications.

License: Creative Commons BY-NC-SA

[fierydino]

The last derivations are just awesome!!😀

[Nox.INkRecords]

Thank you for sharing this. Truly very informative.

[nathanielthomas]

Be warned:

There are several typos on the notes for this lecture, especially around the proof of the chain rule. They're easy to catch, for example, some "y"s should be replaced with "x"s and "x"s should be replaceed with "d"s. Keep it in mind when you're following along. Likely the notes were taken in real time and not proofread, which isn't atypical for a student following a lecture. Otherwise, they are very good LaTeX notes.

[hakus]

37:07 I believe it should be yn converging to c not xn

[almche]

Thank you a lot . also we need physical organic chemistry .because chemistry subjects in channel is a few

[abdiqanifarah]

It seems the chap is talking to himself, and those filming seem to be doing so for falcons. Cheers

[lordmegatron]

What is written on the board is not clear

[almche]

Thank you. Please we need Organometallic Chemistry .tq

[OmidSadeghi]

In minute 1:12:26 he says "it's taboo to write on the back board." Why they don't use the back board and why is it taboo?

[amankumarjha]

Well i can proudly say that in India a normal YouTube channel can explain this much much better than this one

[necmettinkararer]

Ey insanlar!
Sizleri, nefsinize KUL OLMAKTAN ;
ALLAH'A KUL OLMAYA DAVET EDİYORUM.
UNUTMAYALIM Kİ;
"'LA İLAHE İLLALLAH MUHAMMEDURRASULULLAH" DEYİP KALBİMİZLE İMAN ETMEDİKÇE DÜNYADA DA AHİRETTEDE kurtuluş yoktur.

[AnujKumar-bwbg]

I think Indian teachers are far better than mit teachers. And we study this in our 12 grade.

[gautamproductionhouse]

Our indian teachers are best.
Jai hind
Our teaching style is best as it is both side interaction.

[MANIAC-zc]

in 36:50, why sequences are defined by c + delta/2n? why not just delta/n? is there reason you divide 2?