Chain rule for partial derivatives of multivariable functions (KristaKingMath)
Вставка
- Опубліковано 21 вер 2024
- ► My Partial Derivatives course: www.kristaking...
Learn how to use chain rule to find partial derivatives of multivariable functions.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
FACEBOOK // / kristakingmath
TWITTER // / kristakingmath
INSTAGRAM // / kristakingmath
PINTEREST // / kristakingmath
GOOGLE+ // plus.google.co...
QUORA // www.quora.com/...
I hit a mental block trying to understand this chain rule for the past few hours. Books were useless and I nearly gave up. Then came across your suggestion to use a tree to write out the individual variables. I can't believe I have now finished all exercises involving this chain rule for partial derivatives of multivariable functions part. Thank you so much.
That makes me happy! I'm so glad I can help along the way! :)
This Tree Method to solve these complex Derivatives is OSCAR WINING METHOD
💯 💯
I have always struggled whit how to set up the chain rule under different conditions and had never seen the tree-trick. I am shore that will help me a lot in the future. Thanks for the grate video
+jovaha You're welcome, I'm glad it helped!
hello shore, I'm ocean.
**waves**
you are such an inspirational teacher and it helps that your voice is smooth as silk
You don't find such well explained videos these days, very well done and thanks.
Thanks, Sebastian!
@@kristakingmath i like your voice.
Thanks a million... you've explained abstract stuff in a realistic manner. helped me a great deal
You're welcome, I'm so glad it helped!
your voice is so nice that it makes multidimensional calculus so easy to understand
That was 2 hours worth of lectures in 15 minutes. Thanks loads!
I'm so glad it helped! :D
you are just so clear, until now, dint realize that this was actually simpler than the books put it. thankyou Krista!
you're welcome!
Without you I would have failed my midterm indefinitely but I earned a solid A with you videos. I really hope you continue to make more because you are very much appreciated!!!
+Arianna Manabat Awww thank you so much! Congratulations on such a good grade, I'm so happy for you!!
This is excellent. I love how it didn't only teach how to crunch it out, but that you actually explained why.
Thanks Ahmed!
OMG you explained so clearly!! Do you have videos on all Calculus 3 topics? This is life savior lol
yes she do.
awesome lecture and VOICE....yes, your voice is so pleasing to hear and you make your lectures so easy to comprehend. I thank you so much for sharing your knowledge with us that cannot afford to pay lol, but true.
That tree trick is so killer! much better than memorizing anything. Thank you so much for this video!
+TheCarbonMirror I agree, you're welcome!
You ma'am, are my hero. I had no idea what my professor was going on about. Thank You!
+Aaya Khalid I'm glad I could help!
14:38 You can go twice as fast by noting that r and theta are symmetrical with respect to s and t. (s and t can be interchanged without affecting the formulas for r and theta) So, once you have partial (z/t) you can get partial (z/s) by swapping t and s, so partial (z/s) = partial (z/t)[t s]
(I only saw that when I saw both end results, then I figured out why that is)
If only one could like and subscribe more than once. You are one of my favorite youtube teachers.
everytime I go on you tube you have a video that is going over Exactly what we are in class I have hw over chain rule derivatives today :)
This is still helping years later! Exam on this tomorrow.
Thank god for Krista King, without you people with crappy professors would be screwed all around
I'm not taking the class anymore....but a run a community college math center. Your plane and easy explanations are being passed on to my students. Thanks. Some things I know...I can't explain simply. :)
the trick with the tree is amazingly powerful and simple. thank you very much :)
It helps me too! :) Glad you liked it.
Only of my teachers as good as you...I would ace my every stupid exam...Very good job..Keep going!
I'm so glad I can at least help through the videos! :)
Amazing explanation. I was very confused by the different cases and didn't understand the differences in variable dependence until seeing this.
Great video! My prof flew through this material in the last 5 min of lecture. Thanks!
You're welcome, I'm happy to help! :)
that little chalk is soooo cute. it makes learning math 1000x more enjoyable LOLOL
thank you for the clear explanation!
I really like your explanation, it's very clear
Thank you!
amazing maam,, just started partial differentiation, the concept of partial differentiation of composite functions and total differentiation is awesome. loved it.. 😇
So clear and simply. I wish I could have liked this video ten times. Thank you so much.
Aw thanks Natalie! I still really appreciate the 1 like. Glad it could help! :D
Yes, I would definitely recommend the academy, especially for calc 2. Differential equations is more of a work in progress at the moment. If you go to my website, you can now sign up and try the courses for free. :)
THANK U SO MUCH!!!!!!!!!!!!!!!!!!!!!!!!!! THANK YOU ANGEL ! U MADE MY LIFE A BETTER ONE!
This is the best way to solve with multi variable chain rule. I like the the tree diagram it solves everything! Great job! Keep it up.
Thanks, Mohammed! I love the tree diagram too! :D
Very nice job. After following you through the case 1 and then explaining that there were two solutions to the second, I was able to do the second one before verifying it with the video. The tree really helps! Thanks!
Awesome! Great job, I'm so glad this helped!! :D
complete, clean, very good exposition; congratulations! Suggestion: do a video on partial derivative properties, like the cyclic rule.
Thanks for the suggestion Alexandre! :)
I think I'm pretty lucky that my professor is really good, but your videos make the sections so much more understandable. Thank you! :-D
Aha, now I see why sometimes it is dx/dt and sometimes partial dx/dt. Simple when you know, but thanks for telling me! Great video.
Thank you!!! The tree diagram really cleared things up for me.
Very clear explanation. Thank you very much.
+Jhonatan Becerra You're welcome, I'm so glad you liked it!
Mam you are good maths teacher❤😊
You make this so clear! Impressive. I wish you were my calc teacher...
Aw thanks! I'm glad I can help!
I like your way of teaching really you did your best thanks
YOU ARE A FANTASTIC TEACHER!
MY COMPLIMENT
Everything is so clear. All your videos are great, thanks!
You're welcome, I'm so glad they're helping!
Your videos are educationally awesome 😁
Shouldn't your case I example be a regular derivative? Not a partial derivative?
@James Gardiner How would you take the regular derr of that function when there are 3 variables. You would need to use partial derrivatives. No ?
your right, she made a mistake
I think so yes. You cal that a total derivative.
The tree diagram really helped a lot, I haven't seen it before. Thanks for the great video! :)
+Sidd B Thanks! I really appreciate the comment.
In a rare criticism of the best math teacher. (probably the best teacher, period) on UA-cam, my head starts to spin at the beginning of the where 2 examples are compared / contrasted while introducing the concept multiple dependent /independent variables. I would have been better off if this were two separate videos, one for each example.
Also, the popups at the start of the videos are just a distraction, and make learning from these otherwise excellent videos harder. Anyone/everyone who shows up here in first place knows there's more good stuff on Krista's website - "how could there not be?" when so much effort has gone into making this the best math teaching device, probably in the history of the world. Why slow down the student's progress with unnecessary pop ups?
thank u soooo much .. finally i understood this lesson which i couldnt for three lectures .. thx 2 u ..
Yay! I'm so glad I could help. :)
Thank you so much! You are a fantastic prof!
Your teaching is so good. Thank you!
underrated. you're amazing krista
Thank you so much for the explanation. You're a lifesaver!
It's so wonderful and kind of you to share your math expertise with the world! Your videos are amazing! I can't wait to watch all of them over winter break just because they're so great! Thanks again! I'm taking linear differentials next semester. Do you have any videos on this topic? That would be neat-o! You're such a great teacher and you have a wonderful energy when you present things please never stop! :-)
Thank you! for the wonderful explanation. Helped me a lot.
+Relson Deo So glad I could help!
These videos are a huge lifesaver. Question about the second example: At the end, shouldn't we substitute r and theta with their values at the end?
Thanks
Miss or Ma'm you've cleared my needs and doubts. It was so helpful. May the Lord bless you with more 'talents'
thank u teacher you have save my lot of important time .......
Man I thought the chain rule was suppose to make things easy. I guess it does here but damn that is a long process for two variables. I think this video is going to save me some time. I just wonder if a professors actually expect students to remember this in say a year after taking this class. With all the formulas for directional derivatives and finding tangent planes this is a lot to remember.
Wow you explained it so clearly thank you so much, keep on doing more videos like this.
your voice is so calming:) thanks for the vid~!
You're welcome!
VERY helpful. exactly what I needed.
many thanks
Totally understood everything! Thanks a lot! :D
Madhujita Ambaskar I love you
You make so much sense! Thank you so much!
nothingiskool You're welcome, I'm so glad it helped!
It takes time. :) The chalk is replacing the cursor. I explain how I create my videos here: integralcalc . com/how-I-create-my-videos/
Thanks so much for sharing these with your students, I really appreciate it!! :D
Well done. That was a good, clear explanation
+Brad Krupp Thank you very much!
This is so awesome.the best explanation ever...keep it up
marvin tosh Thanks!
welcome... keep it up
this channel is too good to be true...
In case 1, I think it should be dw/dt (ordinary derivative not partial derivative) as w depends totally on t (partially on x and partially on y) and the change in the independent variable t is totally (not partially) responsible for the change in w.
Thank you so much! You explain everything so clearly. Good job!
Thanks, I'm glad it helped!!
integralCALC I wish they would just fire all the math teachers and instead show your videos in math courses.
you are a good teacher, Very Meticulous !
Aw thanks Corey!
I just like the way you explain. Wonderful. will get Ds
you just save my Life as allwayes,tnx for this video
Farhad Farkish you're welcome, i'm so glad it helped!
Cheers from New Zealand!
when you play the video, spam the number "0" and you will hear krista sing TIRI TIRI TIRI TIRI
finally I understand it. Thank you
Clear and concise.👍
Excellent video, many thanks!!
You're welcome, Tara, I'm happy to help! :)
If the original function z is also dependent on the t parameter directly then you have to include dz/dt as well I think.
Flawless explanation!!
Aw thanks! I'm glad you liked it. :)
Thank you for these superb videos! Really enjoying them.
You're welcome, I'm so glad you're enjoying them! :D
So glad I could help! :)
one thing I don't understand is how do you know that you shout add the branches together? when you go down a branch you multiply which makes sense because of the chain rule, but why do add the branches together?
I have a brief question from the calculus of variations. In one argument they are basically telling me that d/da f(y+an,y'+an',x) = n df/dy + n' df/dy' where y and n are functions of x and a is a real number. This seems wrong to me since we need df/d(y+an) and df/d(y'+an'). Now this is really part of a derivation of the Euler Langrange equations. I suppose that since a is going to zero df/d(y+an)(and its counterpart) go to df/dy because we have to assume that that a goes to zero when y is the shortest path. But still it troubles me this is not stated explicitly...... I hope my interpretation is correct.
thank you
Think it may have bee a little easier to have listed x y z in the first column and w in the second. Knockout presentation!
thank you very much, now all of it makes sense to me
+Phanindra Varma Awesome!
I'm glad I can help! :)
You the real MVP! *clapping*
your voice is amazing
Thank you babe for clear explanation ;)
wait. wait in 12:40 minutes. It should be partial derivative of 'z' w.r.t. 'r' into derivative of 'r' w.r.t. 't'. But it's written mistakenly partial derivative of 'z' w.r.t. 'r' into PARTIAL derivative of 'r' w.r.t. 't' pLease correct me if I am wrong.
Thank you, you just saved my semester :D
Can you take this further and do where all d's are partials (d^2 z)/(drd?) where x=rcos(?) and y=rsin(?) Please?
I understand the partials pretty well but dont understand the partial, chain, product rule all at once, it would be much appreciated!!
Good explanation.
I have a doubt about the limit of a PD. Why does the parcial derivative doesn't exist in the origin when the limit equals (for example) (+/-) 1?
Wow it helped me a lot. Thanks for your excellent teaching skills :)
+Syed Ali Abbas I'm so glad it helped!
So taking the total derivative is just a more comprehensive way of doing product rule substitution?
I'm so glad!! You're welcome!! :D