That makes me happy! I'm so glad I can help along the way! :)
@Hercules0037 жыл бұрын
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.
@jovaha8 жыл бұрын
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
@kristakingmath8 жыл бұрын
+jovaha You're welcome, I'm glad it helped!
@wolfdogw41487 жыл бұрын
hello shore, I'm ocean.
@ashishranjan71756 жыл бұрын
**waves**
@vpr14228 жыл бұрын
You don't find such well explained videos these days, very well done and thanks.
@kristakingmath8 жыл бұрын
Thanks, Sebastian!
@vaibhavgupta9736 жыл бұрын
@@kristakingmath i like your voice.
@tianaiye93128 жыл бұрын
OMG you explained so clearly!! Do you have videos on all Calculus 3 topics? This is life savior lol
@NiggaSlayer6666 жыл бұрын
yes she do.
@batmanvsjoker62595 жыл бұрын
This Tree Method to solve these complex Derivatives is OSCAR WINING METHOD
@lordofmech3 жыл бұрын
💯 💯
@avilcorrea223710 жыл бұрын
Thanks a million... you've explained abstract stuff in a realistic manner. helped me a great deal
@kristakingmath10 жыл бұрын
You're welcome, I'm so glad it helped!
@vor61262 жыл бұрын
you are such an inspirational teacher and it helps that your voice is smooth as silk
@anthonyelenga89397 жыл бұрын
your voice is so nice that it makes multidimensional calculus so easy to understand
@ariannamanabat98328 жыл бұрын
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!!!
@kristakingmath8 жыл бұрын
+Arianna Manabat Awww thank you so much! Congratulations on such a good grade, I'm so happy for you!!
@tt2129211 жыл бұрын
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 :)
@TheVickster9811 жыл бұрын
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-ny6qb7 жыл бұрын
This is excellent. I love how it didn't only teach how to crunch it out, but that you actually explained why.
@kristakingmath7 жыл бұрын
Thanks Ahmed!
@AnimeDiva1239 жыл бұрын
You ma'am, are my hero. I had no idea what my professor was going on about. Thank You!
@kristakingmath9 жыл бұрын
+Aaya Khalid I'm glad I could help!
@OndrejPopp6 жыл бұрын
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)
@MultimodAll4 жыл бұрын
If only one could like and subscribe more than once. You are one of my favorite youtube teachers.
@CHAYITO-ii5pt10 ай бұрын
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-pj2vc4 жыл бұрын
This is still helping years later! Exam on this tomorrow.
@bright6019 жыл бұрын
you are just so clear, until now, dint realize that this was actually simpler than the books put it. thankyou Krista!
@kristakingmath9 жыл бұрын
you're welcome!
@Tomciu198511 жыл бұрын
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
@loller306910 жыл бұрын
That was 2 hours worth of lectures in 15 minutes. Thanks loads!
@kristakingmath10 жыл бұрын
I'm so glad it helped! :D
@mocapuccinos11 жыл бұрын
that little chalk is soooo cute. it makes learning math 1000x more enjoyable LOLOL thank you for the clear explanation!
@TheCarbonMirror8 жыл бұрын
That tree trick is so killer! much better than memorizing anything. Thank you so much for this video!
@kristakingmath8 жыл бұрын
+TheCarbonMirror I agree, you're welcome!
@glennhuang180010 жыл бұрын
THANK U SO MUCH!!!!!!!!!!!!!!!!!!!!!!!!!! THANK YOU ANGEL ! U MADE MY LIFE A BETTER ONE!
@wtfchazpwnt6 жыл бұрын
Amazing explanation. I was very confused by the different cases and didn't understand the differences in variable dependence until seeing this.
@friedrichkarlbauhaus86199 жыл бұрын
YOU ARE A FANTASTIC TEACHER! MY COMPLIMENT
@kristakingmath11 жыл бұрын
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. :)
@inteculus6032 жыл бұрын
amazing maam,, just started partial differentiation, the concept of partial differentiation of composite functions and total differentiation is awesome. loved it.. 😇
@anniechiaroni10 жыл бұрын
Shouldn't your case I example be a regular derivative? Not a partial derivative?
@Dannydefeato254 жыл бұрын
@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 ?
@nushynush88554 жыл бұрын
your right, she made a mistake
@3koningen4 жыл бұрын
I think so yes. You cal that a total derivative.
@meetrealestatemindset8 жыл бұрын
Thank you! for the wonderful explanation. Helped me a lot.
@kristakingmath8 жыл бұрын
+Relson Deo So glad I could help!
@deonpersaud95407 жыл бұрын
So clear and simply. I wish I could have liked this video ten times. Thank you so much.
@kristakingmath7 жыл бұрын
Aw thanks Natalie! I still really appreciate the 1 like. Glad it could help! :D
@amirahhill895110 жыл бұрын
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! :-)
@mohammednagdy66615 жыл бұрын
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.
@kristakingmath5 жыл бұрын
Thanks, Mohammed! I love the tree diagram too! :D
@loveislouderrrrr5 жыл бұрын
underrated. you're amazing krista
@kristakingmath11 жыл бұрын
Thanks so much for sharing these with your students, I really appreciate it!! :D
@merensow2006 жыл бұрын
Miss or Ma'm you've cleared my needs and doubts. It was so helpful. May the Lord bless you with more 'talents'
@kristakingmath11 жыл бұрын
So glad I could help! :)
@mjasz43416 жыл бұрын
Thank god for Krista King, without you people with crappy professors would be screwed all around
@codekiller77710 ай бұрын
Mam you are good maths teacher❤😊
@purecuIt9 жыл бұрын
Thank you so much! You are a fantastic prof!
@fwesterbergh6 жыл бұрын
Thank you!!! The tree diagram really cleared things up for me.
@HANGCKH14 жыл бұрын
Your teaching is so good. Thank you!
@NordicKappa9 жыл бұрын
You make so much sense! Thank you so much!
@kristakingmath9 жыл бұрын
nothingiskool You're welcome, I'm so glad it helped!
@SidddB8 жыл бұрын
The tree diagram really helped a lot, I haven't seen it before. Thanks for the great video! :)
@kristakingmath8 жыл бұрын
+Sidd B Thanks! I really appreciate the comment.
@linneth148 жыл бұрын
Everything is so clear. All your videos are great, thanks!
@kristakingmath8 жыл бұрын
You're welcome, I'm so glad they're helping!
@Captain_Jack5149 жыл бұрын
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
@janthoma72627 жыл бұрын
the trick with the tree is amazingly powerful and simple. thank you very much :)
@kristakingmath7 жыл бұрын
It helps me too! :) Glad you liked it.
@kristakingmath11 жыл бұрын
It takes time. :) The chalk is replacing the cursor. I explain how I create my videos here: integralcalc . com/how-I-create-my-videos/
@WofD210 жыл бұрын
Only of my teachers as good as you...I would ace my every stupid exam...Very good job..Keep going!
@kristakingmath10 жыл бұрын
I'm so glad I can at least help through the videos! :)
@alexandredurand6293 жыл бұрын
complete, clean, very good exposition; congratulations! Suggestion: do a video on partial derivative properties, like the cyclic rule.
@kristakingmath2 жыл бұрын
Thanks for the suggestion Alexandre! :)
@Lex-sr5jo5 жыл бұрын
Your videos are educationally awesome 😁
@benzer27097 жыл бұрын
I really like your explanation, it's very clear
@kristakingmath7 жыл бұрын
Thank you!
@stvnhentzen5 жыл бұрын
Great video! My prof flew through this material in the last 5 min of lecture. Thanks!
@kristakingmath4 жыл бұрын
You're welcome, I'm happy to help! :)
@kristakingmath11 жыл бұрын
I'm glad I can help! :)
@zuhairalsaffar70014 жыл бұрын
I like your way of teaching really you did your best thanks
@cojobro297311 жыл бұрын
VERY helpful. exactly what I needed. many thanks
@MultiCesman10 жыл бұрын
your voice is amazing
@sulemanali40067 жыл бұрын
Wow you explained it so clearly thank you so much, keep on doing more videos like this.
@powertube567110 жыл бұрын
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!
@kristakingmath10 жыл бұрын
Awesome! Great job, I'm so glad this helped!! :D
@madhujita10 жыл бұрын
Totally understood everything! Thanks a lot! :D
@dpyp7 жыл бұрын
Madhujita Ambaskar I love you
@MisterBinx9 жыл бұрын
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.
@malvinitolondo9529 жыл бұрын
This is so awesome.the best explanation ever...keep it up
@kristakingmath9 жыл бұрын
marvin tosh Thanks!
@malvinitolondo9529 жыл бұрын
welcome... keep it up
@kalied37154 жыл бұрын
Thank you so much for the explanation. You're a lifesaver!
@TheVoSh0w7 жыл бұрын
Clear and concise.👍
@3377ahmed3 жыл бұрын
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.
@briandwi25042 жыл бұрын
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.
@breannebash34038 жыл бұрын
You make this so clear! Impressive. I wish you were my calc teacher...
@kristakingmath8 жыл бұрын
Aw thanks! I'm glad I can help!
@kafaitullah44994 жыл бұрын
thank u teacher you have save my lot of important time .......
@MrBradman4198 жыл бұрын
Well done. That was a good, clear explanation
@kristakingmath8 жыл бұрын
+Brad Krupp Thank you very much!
@jhonatanbecerra47718 жыл бұрын
Very clear explanation. Thank you very much.
@kristakingmath8 жыл бұрын
+Jhonatan Becerra You're welcome, I'm so glad you liked it!
@kristakingmath11 жыл бұрын
I'm so glad!! You're welcome!! :D
@fernandoavalos455610 жыл бұрын
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?
@mustimansour800810 жыл бұрын
thank u soooo much .. finally i understood this lesson which i couldnt for three lectures .. thx 2 u ..
@kristakingmath10 жыл бұрын
Yay! I'm so glad I could help. :)
@hg2.7 жыл бұрын
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.
@hg2.7 жыл бұрын
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?
@Bhuyakasha10 жыл бұрын
If the original function z is also dependent on the t parameter directly then you have to include dz/dt as well I think.
@EdMoneyHand8 жыл бұрын
Cheers from New Zealand!
@frostpistol9 жыл бұрын
you just save my Life as allwayes,tnx for this video
@kristakingmath9 жыл бұрын
Farhad Farkish you're welcome, i'm so glad it helped!
@clairl31718 жыл бұрын
your voice is so calming:) thanks for the vid~!
@kristakingmath8 жыл бұрын
You're welcome!
@nathanx.6756 жыл бұрын
this channel is too good to be true...
@monomo19976 жыл бұрын
finally I understand it. Thank you
@dekippiesip10 жыл бұрын
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.
@ronpearson51649 жыл бұрын
So taking the total derivative is just a more comprehensive way of doing product rule substitution?
@jameshobsonusa6 жыл бұрын
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!
@larsjjsral9 жыл бұрын
Thank you so much! You explain everything so clearly. Good job!
@kristakingmath9 жыл бұрын
Thanks, I'm glad it helped!!
@Navhkrin9 жыл бұрын
integralCALC I wish they would just fire all the math teachers and instead show your videos in math courses.
@lesliederrar9718 Жыл бұрын
thank you
@Rancor90009 жыл бұрын
You the real MVP! *clapping*
@omar52506 жыл бұрын
Thank you, you just saved my semester :D
@alecsmith72438 жыл бұрын
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 :-)
@coreyseys87917 жыл бұрын
you are a good teacher, Very Meticulous !
@kristakingmath7 жыл бұрын
Aw thanks Corey!
@merensow2006 жыл бұрын
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.
@chipoemeryrwazireni463710 жыл бұрын
I just like the way you explain. Wonderful. will get Ds
@darrenpeck1568 жыл бұрын
Thank you for these superb videos! Really enjoying them.
@kristakingmath8 жыл бұрын
You're welcome, I'm so glad you're enjoying them! :D
@Maarttiin9 жыл бұрын
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?
@jayyoung9637 жыл бұрын
Flawless explanation!!
@kristakingmath7 жыл бұрын
Aw thanks! I'm glad you liked it. :)
@mathematicsicseandcbse17352 жыл бұрын
Good explanation.
@Max-ii3pj8 жыл бұрын
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.
@kristakingmath8 жыл бұрын
+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-ii3pj8 жыл бұрын
Krista King | CalculusExpert.com Thank you very much, I understand it and I appreciate how you answered to me quickly. Thank you so much.
@teteh43907 жыл бұрын
when you play the video, spam the number "0" and you will hear krista sing TIRI TIRI TIRI TIRI
@user-mw3fg5mp3j8 жыл бұрын
may you make a video about the second derivative with 2 variables using the chain rule thank you
@Rayquesto11 жыл бұрын
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.
@TheButcher587 жыл бұрын
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!
@kristakingmath7 жыл бұрын
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