Chain rule for partial derivatives of multivariable functions (KristaKingMath)

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  • 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...
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КОМЕНТАРІ • 249

  • @Hercules003
    @Hercules003 7 років тому +6

    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.

  • @kristakingmath
    @kristakingmath  11 років тому +7

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

  • @batmanvsjoker6259
    @batmanvsjoker6259 5 років тому +19

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

  • @jovaha
    @jovaha 8 років тому +11

    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

  • @vor6126
    @vor6126 3 роки тому

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

  • @vpr1422
    @vpr1422 8 років тому +5

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

  • @avilcorrea2237
    @avilcorrea2237 10 років тому +6

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

    • @kristakingmath
      @kristakingmath  10 років тому +4

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

  • @anthonyelenga8939
    @anthonyelenga8939 7 років тому

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

  • @loller3069
    @loller3069 10 років тому

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

  • @bright601
    @bright601 9 років тому

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

  • @ariannamanabat9832
    @ariannamanabat9832 8 років тому +1

    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
      @kristakingmath  8 років тому +1

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

  • @Ajay-ny6qb
    @Ajay-ny6qb 7 років тому

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

  • @tianaiye9312
    @tianaiye9312 9 років тому +18

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

  • @CHAYITO-ii5pt
    @CHAYITO-ii5pt 10 місяців тому

    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.

  • @TheCarbonMirror
    @TheCarbonMirror 8 років тому

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

    • @kristakingmath
      @kristakingmath  8 років тому

      +TheCarbonMirror I agree, you're welcome!

  • @AnimeDiva123
    @AnimeDiva123 9 років тому +1

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

  • @OndrejPopp
    @OndrejPopp 6 років тому

    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
    @MultimodAll 4 роки тому

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

  • @tt21292
    @tt21292 11 років тому

    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 :)

  • @Kyle-pj2vc
    @Kyle-pj2vc 5 років тому +1

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

  • @mjasz4341
    @mjasz4341 6 років тому

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

  • @TheVickster98
    @TheVickster98 11 років тому

    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. :)

  • @janthoma7262
    @janthoma7262 7 років тому

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

  • @WofD2
    @WofD2 10 років тому

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

    • @kristakingmath
      @kristakingmath  10 років тому

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

  • @wtfchazpwnt
    @wtfchazpwnt 6 років тому

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

  • @stvnhentzen
    @stvnhentzen 5 років тому

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

  • @mocapuccinos
    @mocapuccinos 11 років тому

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

  • @benzer2709
    @benzer2709 7 років тому

    I really like your explanation, it's very clear

  • @inteculus603
    @inteculus603 2 роки тому

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

  • @deonpersaud9540
    @deonpersaud9540 7 років тому

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

    • @kristakingmath
      @kristakingmath  7 років тому

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

  • @kristakingmath
    @kristakingmath  11 років тому

    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. :)

  • @glennhuang1800
    @glennhuang1800 10 років тому +4

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

  • @mohammednagdy6661
    @mohammednagdy6661 5 років тому

    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
      @kristakingmath  5 років тому

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

  • @powertube5671
    @powertube5671 10 років тому

    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
      @kristakingmath  10 років тому +1

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

  • @alexandredurand629
    @alexandredurand629 3 роки тому

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

  • @Tomciu1985
    @Tomciu1985 11 років тому

    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

  • @briandwi2504
    @briandwi2504 2 роки тому

    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.

  • @fwesterbergh
    @fwesterbergh 6 років тому

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

  • @jhonatanbecerra4771
    @jhonatanbecerra4771 8 років тому

    Very clear explanation. Thank you very much.

    • @kristakingmath
      @kristakingmath  8 років тому

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

  • @codekiller777
    @codekiller777 10 місяців тому +1

    Mam you are good maths teacher❤😊

  • @breannebash3403
    @breannebash3403 8 років тому

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

  • @zuhairalsaffar7001
    @zuhairalsaffar7001 4 роки тому

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

  • @friedrichkarlbauhaus8619
    @friedrichkarlbauhaus8619 9 років тому +12

    YOU ARE A FANTASTIC TEACHER!
    MY COMPLIMENT

  • @linneth14
    @linneth14 8 років тому

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

    • @kristakingmath
      @kristakingmath  8 років тому

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

  • @Lex-sr5jo
    @Lex-sr5jo 5 років тому

    Your videos are educationally awesome 😁

  • @anniechiaroni
    @anniechiaroni 10 років тому +24

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

    • @Dannydefeato25
      @Dannydefeato25 5 років тому +1

      @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
      @nushynush8855 4 роки тому

      your right, she made a mistake

    • @3koningen
      @3koningen 4 роки тому

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

  • @SidddB
    @SidddB 8 років тому

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

    • @kristakingmath
      @kristakingmath  8 років тому

      +Sidd B Thanks! I really appreciate the comment.

  • @hg2.
    @hg2. 7 років тому

    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.

    • @hg2.
      @hg2. 7 років тому

      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?

  • @mustimansour8008
    @mustimansour8008 10 років тому

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

  • @purecuIt
    @purecuIt 9 років тому +2

    Thank you so much! You are a fantastic prof!

  • @HANGCKH1
    @HANGCKH1 4 роки тому

    Your teaching is so good. Thank you!

  • @loveislouderrrrr
    @loveislouderrrrr 5 років тому

    underrated. you're amazing krista

  • @kalied3715
    @kalied3715 4 роки тому

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

  • @amirahhill8951
    @amirahhill8951 10 років тому

    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! :-)

  • @meetrealestatemindset
    @meetrealestatemindset 8 років тому +2

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

  • @Captain_Jack514
    @Captain_Jack514 9 років тому

    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

  • @merensow200
    @merensow200 6 років тому +3

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

  • @kafaitullah4499
    @kafaitullah4499 4 роки тому

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

  • @MisterBinx
    @MisterBinx 9 років тому

    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.

  • @sulemanali4006
    @sulemanali4006 7 років тому

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

  • @clairl3171
    @clairl3171 8 років тому

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

  • @cojobro2973
    @cojobro2973 11 років тому

    VERY helpful. exactly what I needed.
    many thanks

  • @madhujita
    @madhujita 10 років тому +3

    Totally understood everything! Thanks a lot! :D

    • @dpyp
      @dpyp 7 років тому

      Madhujita Ambaskar I love you

  • @NordicKappa
    @NordicKappa 9 років тому +2

    You make so much sense! Thank you so much!

    • @kristakingmath
      @kristakingmath  9 років тому +1

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

  • @kristakingmath
    @kristakingmath  11 років тому

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

  • @kristakingmath
    @kristakingmath  11 років тому

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

  • @MrBradman419
    @MrBradman419 8 років тому +6

    Well done. That was a good, clear explanation

  • @malvinitolondo952
    @malvinitolondo952 9 років тому +2

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

  • @nathanx.675
    @nathanx.675 7 років тому

    this channel is too good to be true...

  • @3377ahmed
    @3377ahmed 3 роки тому

    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.

  • @larsjjsral
    @larsjjsral 9 років тому

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

    • @kristakingmath
      @kristakingmath  9 років тому

      Thanks, I'm glad it helped!!

    • @Navhkrin
      @Navhkrin 9 років тому

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

  • @coreyseys8791
    @coreyseys8791 7 років тому

    you are a good teacher, Very Meticulous !

  • @chipoemeryrwazireni4637
    @chipoemeryrwazireni4637 10 років тому

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

  • @frostpistol
    @frostpistol 9 років тому +1

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

    • @kristakingmath
      @kristakingmath  9 років тому

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

  • @EdMoneyHand
    @EdMoneyHand 8 років тому

    Cheers from New Zealand!

  • @teteh4390
    @teteh4390 7 років тому

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

  • @monomo1997
    @monomo1997 6 років тому

    finally I understand it. Thank you

  • @TheVoSh0w
    @TheVoSh0w 7 років тому +1

    Clear and concise.👍

  • @tree8514
    @tree8514 4 роки тому

    Excellent video, many thanks!!

    • @kristakingmath
      @kristakingmath  4 роки тому

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

  • @Bhuyakasha
    @Bhuyakasha 10 років тому

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

  • @jayyoung963
    @jayyoung963 7 років тому

    Flawless explanation!!

  • @darrenpeck156
    @darrenpeck156 8 років тому

    Thank you for these superb videos! Really enjoying them.

    • @kristakingmath
      @kristakingmath  8 років тому +1

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

  • @kristakingmath
    @kristakingmath  11 років тому

    So glad I could help! :)

  • @fernandoavalos4556
    @fernandoavalos4556 10 років тому

    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?

  • @dekippiesip
    @dekippiesip 10 років тому

    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.

  • @lesliederrar9718
    @lesliederrar9718 Рік тому +1

    thank you

  • @jameshobsonusa
    @jameshobsonusa 6 років тому

    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!

  • @phanindravarma8058
    @phanindravarma8058 9 років тому

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

  • @kristakingmath
    @kristakingmath  11 років тому

    I'm glad I can help! :)

  • @Rancor9000
    @Rancor9000 9 років тому +3

    You the real MVP! *clapping*

  • @MultiCesman
    @MultiCesman 10 років тому +13

    your voice is amazing

  • @dhammikaperera4059
    @dhammikaperera4059 6 років тому

    Thank you babe for clear explanation ;)

  • @merensow200
    @merensow200 6 років тому

    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.

  • @omar5250
    @omar5250 6 років тому

    Thank you, you just saved my semester :D

  • @13prt
    @13prt 9 років тому

    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!!

  • @mathematicsicseandcbse1735
    @mathematicsicseandcbse1735 2 роки тому

    Good explanation.

  • @Maarttiin
    @Maarttiin 9 років тому

    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?

  • @syedaliabbas649
    @syedaliabbas649 8 років тому

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

  • @ronpearson5164
    @ronpearson5164 9 років тому

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

  • @kristakingmath
    @kristakingmath  11 років тому

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