Calculus 3 Lecture 13.5: The Chain Rule for Multivariable Functions

Calculus 3 Lecture 13.5: The Chain Rule for Multivariable Functions: How to find derivatives of Multivariable Functions involving Parametrics and/or Compositions. Focus will be on deriving the Chain Rule and practice of examples.

[commentor]

Universities forget how important mathematics really are. They cut down the hours of lessons and professors just give you the main ideas and formulas, no proofs no nothing. However proofs and deep understanding are what get you beyond just passing the semester's exams. They develop your cause-result imagination and allow you to really cultivate original thinking. Thank you Professor Leonard for giving us a chance to choose to differ and study deeply and pointfully.

[charmendro]

00:00 - Intro to Chain Rule with respect to t
44:00 Examples of Chain Rule w/ t
(Organization Tree Method at 47:00 w/ Ex)
56:20 More Intermediate Variables
1:06:00 More Independent Variables
1:10:00 Examples of "More Independent Variables"

[altair]

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[makisxatzimixas]

In case you didn't know, professor, English is not even my native language, yet I'm watching your videos instead of my professor's, because you are so smooth and clear with math. It always make me feel like I can follow without sacrificing any comprehension. If I don't, you make it clear what section of your previous videos I should revise.

[charansingh]

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[gillianpoe]

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[awkward_is_my_superpower]

Professor, I am currently taking Calculus 3. I am an engineering student at the University of Alaska. I sat through the lecture on this topic today. I have never been so confused. Usually my professor does a pretty good job but today it just didn't click. I was pretty worried about my understanding. I watched this video and now I understand. Thank you for this Professor. :-)

[aderitocorreiavaz]

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[OpsBoy]

I started loving calculus after watching your videos, Professor Leonard. I've never thought it would be this interesting
Thank you very much for the fun and interesting videos

[satellite_anomaly]

"I watched Leonard on one half speed..." Cracked me up. Understanding this chain rule material is incredibly useful for pretty much any kind of higher physics and diff eqs. Fantastic work.

[willm]

He has got to be the best math professor of all time, I just finished all my math classes for engineering and I can say without question, he is the best math teacher I have ever seen

[jalaicaann]

MY WHOLE LIFE i never got excited about math till this DAY that changed. The way he shows proofs are so interesting and i seriously wanna keep listening. Your students are so lucky, my professor for calc3 literally reads word per word off of a power point.

[alis]

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[TheNaz]

I love this guy, really explains the math in a manner that is digestible by the student. Wish i had a prof like him.

[AkimboFennec]

Professor LEonard, I came to this video about multi variable chain rule from MIT Open course Ware Denis Aoroux lecture. Some of the lectures that Denis aoroux gave, particularly on second derivative test and the gradient vector were not clear to me. I really enjoyed your explanation about how the chain rule actually works, around 25:00. The best explanation ever, because it is very simply explained, instead of using fancy mathematical words and symbols. This demonstrates that you sir absolutely dominate your field, and you have a talent for a very clean explanation. Thank you very much.

[ninakruzo]

Watching your videos helped me a lot. I didn't understand what was going on in class. Since the topics are somewhat related to one another, I thought I was doomed. Watching your videos helped me a lot. I got an A- for Calculus. THANK YOU.

[caseyj]

I LOVE how much he cares if people understand.

Most teachers: If that didn't make sense, you're broken.

Prof L: Did everyone understand that?? Everyone??

[gfferre]

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