Chains f(g(x)) and the Chain Rule
ฝัง
- เผยแพร่เมื่อ 14 ก.ย. 2010
- Chains f(g(x)) and the Chain Rule
Instructor: Gilbert Strang
ocw.mit.edu/highlights-of-calc...
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
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Dr. Strang's lecture style is among the most delightful I've ever encountered, and as others have commented, his knowledge of subject and student is unsurpassed. Thanks for taking the 'hard' away from learning this most useful tool.
This professor is such a character. I like it. Easy to watch.
Prof Strang's MIT series on Linear Algebra is one of the best math series I've experience.
Trying to spend time to understand chains rule many times.As I follow this lecture grateful Dr. Strang for his understanding the students difficulties in this topic.Thanks a lot.
I have seen a LOT! BUT THIS IS THE BEST LECTURE I HAVE EVER SEEN. FINALLY A TEACHER WHO UNDERSTANDS AND WANTS OTHERS TO UNDERSTAND.
A REAL TEACHER!
REALLY AMAZING. 10 OUT OF 10.
He reiterates points that are important. Amazing instructor
the insight this man has; major respect! thinking about all the hours he has put in his work to be able to understand so well what he is doing! #goals
I need to send MIT OCW some money because even though I studied this stuff for more than 5 years, I am still learning something new or from a different perspective, thanks to Prof. Strang! I love calculus, and listening to the professor, is like listening to a fascinating story or piece of literature.
Thank you! I finally understood much better this important rule. Fantastic teacher and institution!
Thank you Professor Strang....you make unemployment a self actuating adventure!
One of the finest professor's around. Great work as always, Professor Strang.
These lecture series is best lectures on Calculus. Thank you Dr. Strang
Thank you so much Professor Strang for sharing your lectures and knowledge. I have been struggling with the chain rule but after watching this video I have finally finished my homework with a clear understanding of each problem. Your explanation of Leibniz notation is wonderful too. You are a fabulous teacher and I look forward to watching your other videos to supplement my instructor's lectures.
Thank you for your video. I have learned so much from you than the other professors I have encountered that make it hard to understand this subject.
every minute of this series is a ''a-ha'' moment
Grandpa really knows the stuff he is talking about.
@ 24:23 "...this darn finite chalk".
Hahaha....mindblow. Can't believe I missed this.
Would be a great 'Thinkgeek' T-shirt slogan.....
@@geoninja8971 or a name of a metal band
really man, its really blissful that teaching differs from person to person and you can clearly see why XD
He is the best, cool guy, his presence takes MIT to next level,
Gilbert Strang..a great mathematician ..thank you
Although I knew the rules but the perspective that I am able to discover now apart from just doing the calculations is pretty amazing.😊😊
finaly a professor that speaks ENGLISH!!!
Funny! I remember walking into the first lecture of my Differential Equations class...first it was in a large lecture hall, second it was taught by a TA with a VERY strong accent. After that first lecture I switched to another class...which turned out to be small (10-12 students) and taught by a full professor. Best decision ever...Diff Eq was difficult enough!
I was surprisingly entertained for the first time watching this calc video...not even professor leonards videos made me feel the way this man did explaining the chain rule BUT i still enjoy professor leonards videos he's saving my ass. Glad i was able to find another good calc lecturer on youtube though.
thanks for all your informative videos. you are a huge help!
Really , you are the best teacher. Thank you very much!
brilliant lecture as always.
thx so much professor strang.
This is really helpful! Thank You! :)
Amazing teaching style!
"This Darn finite chalk" cant draw a line to infinity.
wow... all of a sudden I see the LIGHT! :) Thank you.
Fantastic!
Just Beautiful---
This guy is awesome.............
Speechless ❤❤ Amazing lecture 😀😀😀🙌
DR. Strang, I learned something new every time I watched your videos.
I love this man such a beautiful man
muchas gracias esto es muy útil
Don't sleep on this just because of the old school blackboard! There are some really good practice problems here!
(At 15:00+): It might be helpful to explicitly show where the chain rule is coming from:
We are given the facts (using "D" for finite steps):
1. Dz = a*Dy (a = Dz/Dy)
2. Dy = b*Dx (b = Dy/Dx)
Insert 2. into 1. to get:
3. Dz = a* b * Dx (this step already reveals the nature of the derivative)
Write out a and b as ratios in 3.:
4. Dz = Dz/Dy * Dy/Dx * Dx
Divide 4. by Dx to get the ratio we are after:
5. Dz/Dx = Dz/Dy * Dy/Dx
Now let "D go to d" (the calculus step) to get the derivative:
6. dz/dx = dz/dy * dy/dx
This is Gilbert strang!
Wish I'd had a lecturer like this in my college days.
Thanks Professor
Good stuff
best mathematics teacher
Why so few views? I really like the way he explains.
I attempted to solve the challenge at the end of the lecture.
I think it would be
d2z/dx^2=d/dx (dz/dy. dy/dx) =d2z/(dx.dy) . dy/dx + dz/dy . d2y/dx^2
I tried it for the example z = (x^2)^3 and it worked
This is the best
McLovin's grandfather...
Dr. Strang seems to be the Mr. Rodgers of Higher Mathematics
Days on Khan Academy.... Progress increased by 5%
35 minutes and 20 seconds here..... "Your BR41N Levelled up to LV. 100"
Khan likes to hear himself talk. I go elsewhere, this video is great!
That's ok but that guy is unique
Thanks.
at 24:40, The graph symmetry in y axis?
At 10:12, when he replaces 2y with x, he replaces the entire term with x^3 instead of 2(x^3). Why is that?
+Carlee Miller (2x^3)(3x^2) is what he did. but he did the (2)(3) by itself at the beginning then moved onto the X itself. If that helps
I wish he was my professor!
after a few mins i was already lost...
This is the kinda of education at mit, also prof.Lewin
Draws better than my calculus professor.
There should be a manga series "GTS" -- Great Teacher Strang. (Obscure reference.) Totally cool stuff.
I know that this comment is years old, but I totally get the reference. Well done, my dear friend, well done.
Here is another fellow who understood the reference.
I just think of it like a Composite Function. It was a fun lesson to be frank.
What a guy!
The Mr. Rogers of Math.
Sorry for being dumb,but I can't get why he multiplies dz/dy by dy/dx. I really can't, and I know it's basic. Anyone,please?
Think about it in terms of its limits, if y doesn’t change at all with changing x then z wouldn’t change with x and that is true from the formula because dy/dx will be zero. Or you can see it from the fact that x doesn’t have direct access to z, so it affects y first then y affects z and that is reflected in the product of the ratios, you can imagine real applications like if something setting inside a box and the box is inside a car, normally its movement ( change in its position ) will effect the box first then affects the car.
This teacher is funny
It's a Hollywood action movie, not mathematics! You don't know what will happen in the end! You Just want to watch it till the end!
I dont understand yet
Noice 👍
i wonder why so less views...???
This Is Easy!
Surely this is not university level?
In a three-semester course in calculus, this would be somewhere around the third or fourth week of the first semester. (First week discussing limits, second week discussing the derivatives of basic functions...) This class assumes no prior experience with calculus prior to college.
I'm so confused.
Yup.
How ?
Calculus is NOT easy! It is extremely rewarding...all of modern physics (Isaac Newton co-discoveded calculus) is based on it, and (as Dr. Strang mentions) a good deal of statistics is based on it.