Chain rule for partial derivatives of multivariable functions (KristaKingMath)

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.

you deserve a Nobel prize for your perfect explanations!! , Krista

That makes me happy! I'm so glad I can help along the way! :)

This is excellent. I love how it didn't only teach how to crunch it out, but that you actually explained why.

You don't find such well explained videos these days, very well done and thanks.

If only one could like and subscribe more than once. You are one of my favorite youtube teachers.

you are such an inspirational teacher and it helps that your voice is smooth as silk

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)

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!

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!!!

You ma'am, are my hero. I had no idea what my professor was going on about. Thank You!

Thanks a million... you've explained abstract stuff in a realistic manner. helped me a great deal

underrated. you're amazing krista

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

OMG you explained so clearly!! Do you have videos on all Calculus 3 topics? This is life savior lol

you are just so clear, until now, dint realize that this was actually simpler than the books put it. thankyou Krista!

that little chalk is soooo cute. it makes learning math 1000x more enjoyable LOLOL
thank you for the clear explanation!

Mam you are good maths teacher❤😊

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!

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 :)

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. :)

Thank god for Krista King, without you people with crappy professors would be screwed all around

This is still helping years later! Exam on this tomorrow.

So clear and simply. I wish I could have liked this video ten times. Thank you so much.

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

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.

amazing maam,, just started partial differentiation, the concept of partial differentiation of composite functions and total differentiation is awesome. loved it.. 😇

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! :-)

Amazing explanation. I was very confused by the different cases and didn't understand the differences in variable dependence until seeing this.

Everything is so clear. All your videos are great, thanks!

The tree diagram really helped a lot, I haven't seen it before. Thanks for the great video! :)

YOU ARE A FANTASTIC TEACHER!
MY COMPLIMENT

Thank you!!! The tree diagram really cleared things up for me.

So glad I could help! :)

Your teaching is so good. Thank you!

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. :)

Wow you explained it so clearly thank you so much, keep on doing more videos like this.

Only of my teachers as good as you...I would ace my every stupid exam...Very good job..Keep going!

THANK U SO MUCH!!!!!!!!!!!!!!!!!!!!!!!!!! THANK YOU ANGEL ! U MADE MY LIFE A BETTER ONE!

Your videos are educationally awesome 😁

I'm glad I can help! :)

Thank you so much for the explanation. You're a lifesaver!

Thank you, you just saved my semester :D

the trick with the tree is amazingly powerful and simple. thank you very much :)

your voice is so calming:) thanks for the vid~!

You make so much sense! Thank you so much!

Miss or Ma'm you've cleared my needs and doubts. It was so helpful. May the Lord bless you with more 'talents'

Great video! My prof flew through this material in the last 5 min of lecture. Thanks!

I really like your explanation, it's very clear

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!

VERY helpful. exactly what I needed.
many thanks

Thank you! for the wonderful explanation. Helped me a lot.

Totally understood everything! Thanks a lot! :D

complete, clean, very good exposition; congratulations! Suggestion: do a video on partial derivative properties, like the cyclic rule.

I like your way of teaching really you did your best thanks

Thank you so much! You are a fantastic prof!

This is so awesome.the best explanation ever...keep it up

Thanks so much for sharing these with your students, I really appreciate it!! :D

Clear and concise.👍

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

you just save my Life as allwayes,tnx for this video

You make this so clear! Impressive. I wish you were my calc teacher...

this channel is too good to be true...

Thank you for these superb videos! Really enjoying them.

Thank you so much! You explain everything so clearly. Good job!

same chick who made the hilarious "Things never overheard in a calc class"? Keep up the great work - clear explanations and love to show my classes more girls being smart :-)

Shouldn't your case I example be a regular derivative? Not a partial derivative?

finally I understand it. Thank you

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.

Wow it helped me a lot. Thanks for your excellent teaching skills :)

It takes time. :) The chalk is replacing the cursor. I explain how I create my videos here: integralcalc . com/how-I-create-my-videos/

thank u soooo much .. finally i understood this lesson which i couldnt for three lectures .. thx 2 u ..

Flawless explanation!!

you are a good teacher, Very Meticulous !

Well done. That was a good, clear explanation

Cheers from New Zealand!

I'm so glad!! You're welcome!! :D

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.

when you play the video, spam the number "0" and you will hear krista sing TIRI TIRI TIRI TIRI

Thank you babe for clear explanation ;)

your voice is amazing

thank you

Excellent video, many thanks!!

You the real MVP! *clapping*

In a rare criticism of the best math teacher. (probably the best teacher, period) on RUclips, 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.

I just like the way you explain. Wonderful. will get Ds

Really good one!

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.

Awesome, clear, 10/10

thank you very much, now all of it makes sense to me

love your videos🖤

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.

You are amazing! Thank you!!!!!!

Thanks for the videos....a question? why does the left hand side of the expression for chain rule not equal the right hand side of expression. The right hand is twice the value of the left hand side if you cancel the appropriate terms. Don't understand......any clarification would be appreciated. Thanks.

o nice
you are best teacher this session for me
thanks alot

If the original function z is also dependent on the t parameter directly then you have to include dz/dt as well I think.