Chain rule for partial derivatives of multivariable functions (KristaKingMath)

[@kristakingmath]

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

[@Hercules003]

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.

[@jovaha]

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

[@kristakingmath]

+jovaha You're welcome, I'm glad it helped!

[@wolfdogw4148]

hello shore, I'm ocean.

[@ashishranjan7175]

**waves**

[@vpr1422]

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

[@kristakingmath]

Thanks, Sebastian!

[@vaibhavgupta973]

@@kristakingmath i like your voice.

[@tianaiye9312]

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

[@NiggaSlayer666]

yes she do.

[@batmanvsjoker6259]

This Tree Method to solve these complex Derivatives is OSCAR WINING METHOD

[@lordofmech]

💯 💯

[@avilcorrea2237]

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

[@kristakingmath]

You're welcome, I'm so glad it helped!

[@vor6126]

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

[@anthonyelenga8939]

your voice is so nice that it makes multidimensional calculus so easy to understand

[@ariannamanabat9832]

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!!!

[@kristakingmath]

+Arianna Manabat Awww thank you so much! Congratulations on such a good grade, I'm so happy for you!!

[@tt21292]

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 :)

[@TheVickster98]

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. :)

[@Ajay-ny6qb]

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

[@kristakingmath]

Thanks Ahmed!

[@AnimeDiva123]

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

[@kristakingmath]

+Aaya Khalid I'm glad I could help!

[@OndrejPopp]

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)

[@MultimodAll]

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

[@CHAYITO-ii5pt]

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.

[@Kyle-pj2vc]

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

[@bright601]

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

[@kristakingmath]

you're welcome!

[@Tomciu1985]

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

[@loller3069]

That was 2 hours worth of lectures in 15 minutes. Thanks loads!

[@kristakingmath]

I'm so glad it helped! :D

[@mocapuccinos]

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

[@TheCarbonMirror]

That tree trick is so killer! much better than memorizing anything. Thank you so much for this video!

[@kristakingmath]

+TheCarbonMirror I agree, you're welcome!

[@glennhuang1800]

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

[@wtfchazpwnt]

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

[@friedrichkarlbauhaus8619]

YOU ARE A FANTASTIC TEACHER! MY COMPLIMENT

[@kristakingmath]

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. :)

[@inteculus603]

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

[@anniechiaroni]

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

[@Dannydefeato25]

@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 ?

[@nushynush8855]

your right, she made a mistake

[@3koningen]

I think so yes. You cal that a total derivative.

[@meetrealestatemindset]

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

[@kristakingmath]

+Relson Deo So glad I could help!

[@deonpersaud9540]

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

[@kristakingmath]

Aw thanks Natalie! I still really appreciate the 1 like. Glad it could help! :D

[@amirahhill8951]

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! :-)

[@mohammednagdy6661]

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.

[@kristakingmath]

Thanks, Mohammed! I love the tree diagram too! :D

[@loveislouderrrrr]

underrated. you're amazing krista

[@kristakingmath]

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

[@merensow200]

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

[@kristakingmath]

So glad I could help! :)

[@mjasz4341]

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

[@codekiller777]

Mam you are good maths teacher❤😊

[@purecuIt]

Thank you so much! You are a fantastic prof!

[@fwesterbergh]

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

[@HANGCKH1]

Your teaching is so good. Thank you!

[@NordicKappa]

You make so much sense! Thank you so much!

[@kristakingmath]

nothingiskool You're welcome, I'm so glad it helped!

[@SidddB]

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

[@kristakingmath]

+Sidd B Thanks! I really appreciate the comment.

[@linneth14]

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

[@kristakingmath]

You're welcome, I'm so glad they're helping!

[@Captain_Jack514]

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

[@janthoma7262]

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

[@kristakingmath]

It helps me too! :) Glad you liked it.

[@kristakingmath]

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

[@WofD2]

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

[@kristakingmath]

I'm so glad I can at least help through the videos! :)

[@alexandredurand629]

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

[@kristakingmath]

Thanks for the suggestion Alexandre! :)

[@Lex-sr5jo]

Your videos are educationally awesome 😁

[@benzer2709]

I really like your explanation, it's very clear

[@kristakingmath]

Thank you!

[@stvnhentzen]

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

[@kristakingmath]

You're welcome, I'm happy to help! :)

[@kristakingmath]

I'm glad I can help! :)

[@zuhairalsaffar7001]

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

[@cojobro2973]

VERY helpful. exactly what I needed. many thanks

[@MultiCesman]

your voice is amazing

[@sulemanali4006]

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

[@powertube5671]

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!

[@kristakingmath]

Awesome! Great job, I'm so glad this helped!! :D

[@madhujita]

Totally understood everything! Thanks a lot! :D

[@dpyp]

Madhujita Ambaskar I love you

[@MisterBinx]

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.

[@malvinitolondo952]

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

[@kristakingmath]

marvin tosh Thanks!

[@malvinitolondo952]

welcome... keep it up

[@kalied3715]

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

[@TheVoSh0w]

Clear and concise.👍

[@3377ahmed]

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.

[@briandwi2504]

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.

[@breannebash3403]

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

[@kristakingmath]

Aw thanks! I'm glad I can help!

[@kafaitullah4499]

thank u teacher you have save my lot of important time .......

[@MrBradman419]

Well done. That was a good, clear explanation

[@kristakingmath]

+Brad Krupp Thank you very much!

[@jhonatanbecerra4771]

Very clear explanation. Thank you very much.

[@kristakingmath]

+Jhonatan Becerra You're welcome, I'm so glad you liked it!

[@kristakingmath]

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

[@fernandoavalos4556]

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?

[@mustimansour8008]

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

[@kristakingmath]

Yay! I'm so glad I could help. :)

[@hg2.]

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

[@hg2.]

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?

[@Bhuyakasha]

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

[@EdMoneyHand]

Cheers from New Zealand!

[@frostpistol]

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

[@kristakingmath]

Farhad Farkish you're welcome, i'm so glad it helped!

[@clairl3171]

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

[@kristakingmath]

You're welcome!

[@nathanx.675]

this channel is too good to be true...

[@monomo1997]

finally I understand it. Thank you

[@dekippiesip]

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.

[@ronpearson5164]

So taking the total derivative is just a more comprehensive way of doing product rule substitution?

[@jameshobsonusa]

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!

[@larsjjsral]

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

[@kristakingmath]

Thanks, I'm glad it helped!!

[@Navhkrin]

integralCALC I wish they would just fire all the math teachers and instead show your videos in math courses.

[@lesliederrar9718]

thank you

[@Rancor9000]

You the real MVP! *clapping*

[@omar5250]

Thank you, you just saved my semester :D

[@alecsmith7243]

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 :-)

[@coreyseys8791]

you are a good teacher, Very Meticulous !

[@kristakingmath]

Aw thanks Corey!

[@merensow200]

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.

[@chipoemeryrwazireni4637]

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

[@darrenpeck156]

Thank you for these superb videos! Really enjoying them.

[@kristakingmath]

You're welcome, I'm so glad you're enjoying them! :D

[@Maarttiin]

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?

[@jayyoung963]

Flawless explanation!!

[@kristakingmath]

Aw thanks! I'm glad you liked it. :)

[@mathematicsicseandcbse1735]

Good explanation.

[@Max-ii3pj]

at 10:50 , the partial derivative of (S^2+t^2) with respect to S, you said it is just 2S, but isn't it 2S+t^2, because we take t^2 as a constant and it will be there forever. you also used the same way at 13:33 please help me if you know it.

[@kristakingmath]

+MIMBUBA When you take the derivative of a constant, it's 0. In the same way that the derivative of x^2+3x+7 is 2x+3+0, or just 2x+3. The derivative of the constant 7 is 0, so that terms drops away. And it's the same thing here... when you take the derivative of the constant t^2, the derivative is 0. I hope that helps!

[@Max-ii3pj]

Krista King | CalculusExpert.com Thank you very much, I understand it and I appreciate how you answered to me quickly. Thank you so much.

[@teteh4390]

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

[@user-mw3fg5mp3j]

may you make a video about the second derivative with 2 variables using the chain rule thank you

[@Rayquesto]

Ah. Well, the tree diagram makes everything simple. I remember my teacher tried generalizing the whole process using matrix solutions, but that was far too complex. I could have memorized it, but I am not good with Matrices yet. So, what if we have a function f(x, y, z) and we want to find devx/devxdevy?...Well, I suppose we could use the chain rule simply with the tree diagram right? I'll try it out. I thought the only way was the matrix way.

[@TheButcher58]

I have a question: In my book there are different exercises which ask the partial derivative like this: (d^2*z)/(d*s^2) the d is the weird d in the partial derivate. My question is: what kind of difference does the power 2 make, because I couldn't understand the way they did it in the answers? Btw: your videos are very helpful and I liked and subscribed to support you!

[@kristakingmath]

The 2 power indicates that you're talking about the second derivative. So, dz/ds is the first derivative, meaning the derivative of z with respect to s. But when you've got that squared power, it means the second derivative of z with respect to s. I hope that makes sense, and thank you so much for your support! :D