❖ General Chain Rule And Partial Derivatives ❖

[@brandonspike]

I was 13 years old taking algebra 1 when this video was published. Now I'm 20 years old, taking multivariable calculus, and i couldn't be happier that i found this channel. You're awesome, Patrick!

[@asemnafiz]

Hope this video stays when your children are taking multivariable calculus.

[@patrickjmt]

asemnafiz they wont need the video, they will have me!

[@ExperimentLife]

patrickJMT That doesn't sound right.

[@amer81397]

+Brandon R I'm 18 and taking calc 3 tbh

[@sjard97]

Lol, that's exactly my situations right now.

[@dylanjohnson3734]

MY GOD I UNDERSTAND THIS. When I graduate, I'll pretty much owe my degree to Patrick here.

[@shayman48]

I think we all will....

[@NiggaSlayer666]

Did anyone graduate yet?

[@garnett657]

@@NiggaSlayer666 almost

[@dudeisawesome7202]

@@NiggaSlayer666 2022 hopefully lol otherwise 2023 but this man has been saving me so many times!

[@hmmm0001]

WOW! You explain in 10 mins what my lecturers can't explain in an understandable way in 10 hours. Not only do I pass exams thanks to your vids, I actually learn something too! You absolutely ROCK man! Will donate! :)

[@VegasStreetLights]

I enjoy getting high and then watching all of your videos. Your voice over is perfect for the stoned context. Pretty high right now

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VegasStreetLights wtf dude

[@dont_trust_any1_even_ur_waifu]

wtf??

[@simonharvey7141]

lmfao

[@lindsaycooper16]

Hello, I just want to tell you how thankful I was to come across your channel! I have never been very good at math. When I started Calculus this semester, I came across your channel because I didn't understand anything in the class. You made everything seem so easy to me! I was one of the only two people who made an A on the first test with the class average being a 32. It was definitely a self confidence booster when it comes to math because this has NEVER happened. Thank you so much.

[@TheThirdReigh]

I have spent hours in the traditional college classroom and learned very little. I sit around my computer and watch your videos for 10-15 minutes and I able to understand and solve the problems within minutes. Your videos are excellent, thanks a lot.

[@swissirish1]

From one Patrick to another, you're a lot smarter than me. Also you're v's look a little like square root signs

[@williamreyes3801]

OMG, thank you Patrick. My professor spent 1hr and 30 min trying to explain this and "FAILED" and it only took me 9 min on KZbin to understand it. GO University of Patrick!!!!

[@randomuser6064]

this guy saving my stupid ass since 2014

[@socialistguerrilla773]

shame that youre nazi trash

[@randomuser6064]

and you're a human disgrace

[@Aer01614]

But why the hatred when you guys are actually more similar than not. After all you are both socialist. Nazi party was the National SOCIALIST German Workers Party.

[@MrEnglishWorld]

He is also saving mine now, and in future I guess LOL

[@DreamBig2GoBig]

Dude you're actually the best. A textbook can give you the formula, but you always need to learn it at least three different ways to master it conceptually. Your videos are one of my frequent stops.

[@Zyloly]

My textbook is full of jibberish and it takes me 30mins to an hour to finally understand what the heck is going on, but your videos in just approximately 10mins you cover what an hour lecture and of textbook reading would cover..thank you so much..You can be sure once I get my degree and a well paying job I will gladly donate my fair share :) P.S I'm currently studying Computer Science

[@akshaygujjar3113]

Love the tree technique! Makes it so much easier!

[@MrMafala]

I can't thank you enough Patrick, each lecture you give is incredibly helpful and simplified. you awesome man! the only problem is that you are left handed and you obstruct me quite a lot when trying to take notes. LOL. I AM KIDDING.

[@patrickjmt]

No, you are correct, my hand is often in the way but, that's how it goes

[@JoseGuillen422]

thank you Patrick, i owe you so much and a lot of late nights cramming before an exam are spent watching your videos. stay safe, you are a blessing in the youtube world.

[@ibrahimnasir4487]

i was gonna say "I wish you were my prof" an then i realized you already are. you replaced him a long time ago. I'm pretty sure my entire year learns from you more than our actual prof. Thanks so much Patrick, you really are my Hero

[@Eruption1O2]

PatrickJMT: the math savior of the internet.

[@tysterr]

At my university we are doing this in Calculus 4. Patrick, thank you very much for doing these videos. They help more than you probably think.

[@Beatmastapat09]

PatrickJMT is the only dude i support on Patreon and its still paying off! way to go man!

[@HERKFOOT21]

May i also suggest looking up youtube user ProfRobBob, best math teacher i've seen yet!

[@patrickjmt]

thanks! telling others about the videos is the best donation you could make! :)

[@siyuanthesuper1]

Man thanks patrick. you saved my grade since 7th grade. now im in college, and im still watching your videos. thanks very much.

[@amrotarek9893]

I was eight years old when this video was published , and you know what ? This guy teaches mathematics better than my university's professors who gets thousands of pounds every month ! He doesn't have the number of certificates they have but he is better than them ! Thanks Patrick ❤️

[@ahmedismail4743]

Patrick I was watching your videos when I was in elementary school now am doing engineering and your videos are still quite handy to me, may God bless your soul wherever you're now 😊

[@bjdooi]

THE TREE DIAGRAM HELPED ME OUT SO MUCH, I CAN DO THESE WITH MY EYES CLOSED NOW!! THANK YOU SO MUCH PATRICK

[@sincerepjpf5115]

-Thanks so much... ''I'' depend on ''U''

[@alvinramnarine314]

patrick you`re the best dude.keep up the good work.

[@ragedxgamer7923]

I am in love with your teaching methods , even our so called qualified teachers are not able to teach us like your simple tutorials. May God bless you.peace.

[@Chapelthewhite]

That flow chart in the beginning (1:30ish) is a really brilliant way of looking at it! Thank you!

[@TheBaseballman1990]

thank you for this, my teacher just gives up when the harder problems come around, this video is literally the only way i can learn this!

[@patrickjmt]

@MajinAmmaar no, not exactly; i assume you are in first semester calculus, so you are still doing single variable stuff; this has to do with multivariable stuff. technically this applies to what you are doing, but the general power rule is a specific rule versus a general procedure (which this is)

[@parkourepic2D]

finally someone that can explain this without being vague or stuck up!

[@patrickjmt]

nah, just a normal guy making vids on youtube! glad i could help though : )

[@KoolViking3]

Man, you know your maths and you know how to teach it! Thanks a million!

[@pendolly]

panic!panic!i have my first calculus exam coming tuesday.thanx patrick for the good work you do

[@ArtyomMP01]

After 12 yrs your video is among the best

[@wlmngtn310]

Wow, you are simply the greatest! If only all my professors were as good as teaching as you are.

[@akatsukiabima9942]

In less than 10 minutes I learned more here than I learned from my prof during the whole semester.... life is sad

[@ramosk95]

I bought a sharpie because of you!!

[@hadriennouvel2665]

It's "because of u" lmao With my respect to u 😂

[@PiratePrinceEdward]

I've been struggling for this for a bit. You make it look so easy!! Definitely subscribing to this channel. Thank you, seven year old video!

[@amritdhanjal8781]

Patrick I love u keep making math videos and saving my GPA

[@patrickjmt]

yes, you are just using the product rule in essence

[@patrickjmt]

there is a donation link on my channel page if you feel that bad about it... :)

[@patrickjmt]

@n00dl3head happy that i could help you a bit : )

[@hoomanhu]

i miss my most of calculus classes because i know patrick is gonna cover for me:-) thanks man...

[@ncs9334]

Dude u just earned my respect, and a like too!!

[@patrickjmt]

glad you liked the video!

[@Atsuke]

"With respect to u." NO. Respect to YOU, not me. You are a freaking lifesaver.

[@KronesianLTD]

Appreciate it mate, much better explaining it than my professor.

[@patrickjmt]

glad i could help you out :)

[@monicagarcia1104]

i just love how you explain every video .... u make it way easier... thanks a lot

[@DavidJHilt]

I like treating each component as a branch. That's a very clear way to think of it.

[@ludog014]

OMFG, great video man, you just cut down so much studying.... thank you!!!!!!

[@احمدسلام-د6ت2و]

بالعربي شكرا انت الأفضل انت ساعدتني بالرياضيات love you

[@quoctrung2610]

Uploaded in 2008 and still pretty useful in 2019. Please don't remove this video. I think people still need it in 2100.

[@yashvlog8933]

Where were u these days sir!!!!!really made my day......easyyyyy

[@caseyhenderson1465]

Nothing against Khan academy... but I love your videos so much more!! Thank you so much for your videos

[@kyshark1]

Hi Patrick, Your videos are just amazing and is helping me to re-learn some of the basics after almost 10 years of no contact with maths! Thanks. Could you please double check the end part as I'm a bit confused about some of the partial derivaties that you did (specially with constants)? maybe I'm confused...but any help would be great.

[@mashable8759]

Patrick JMT teaching world maths since forever :D

[@Pigrabbit1412]

OMG UR THE BEST!!! U MAKE EVERYTHING EASY TO UNDERSTAND!! THANK YOU SO MUCH!!!

[@88thotho]

i appreciate the way you teach.

[@leocy202]

the du/dv at 8:30 not the 2uv^2 should be we get?

[@patrickjmt]

glad you like my videos :) come back any time!

[@varlikkzloren37]

BEST EXPLANATION EVER

[@jxe1030]

You Make It Look Sooo Easy !!! Amazing Videos Keep It Up !!!!

[@AlinaCrystal]

You are amazing and I don't think you can hear that enough.

[@emrearslan1797]

You're the best I don't know what else to say but I'll just say it one more "YOU ARE THE BEST !! "

[@lanner777]

Wonderful job, made my professors scribbles on the board seem like chicken scratch! Keep up the amazing work!

[@HiThisIsPatrick]

I LOVE YOU THIS MAKES SO MUCH SENSE

[@commanderkool868]

@bfferz in the second example he uses the partial of x to u because x depends on more than one variable, in the first example x only depended upon t so the derivative was used rather than the partial

[@Dusevic]

nooooooooo way the second question was the exact question i needed help with, same variables and everything!

[@J4e8a16n]

Yes! That's clear. Maybe I was ready for it but you for sure trow light in my life. I am ashame not to have draw the tree of implicit differentiation by myself :o)

[@MiaLynify]

Great video! Way better than how my prof taught it.

[@Koralxox]

You have saved my ass on exams sooooo many times. Thank you

[@terrybutler5831]

I'm guessing that it would just be so complicated with having to use the extended Product Rule. But I'd like to hear Patrick's answer, too.

[@XXxlightmarex]

How would I go onto to find the second derivative (d^2z/du^2)?

[@massem100]

great work patrick

[@antney1111]

Why in the frst problem do you do the partial multiplied by the derivative + the partial multiplied by the derivative yet in the second you do the partial multiplied by the partial + the partial multiplied by the partial ? I understand everything but this, thanks !

[@antney1111]

Could anyone explain this ? I have a test at 230 and I understand mostly everything except this.

[@Beatmastapat09]

+Wisal Abdullah that little statement made alot of sense, thanks!

[@eggrollXXXM]

is this really the beginning of calc? because it so, that's amazing.

[@franceschua7712]

YOU ARE THE BEST !! THANK YOU !!!

[@harkerhh]

The chain rule for normal functions is for calculus 1 but this is multivariable calculus (calc. 3 in my U) so its a different chain rule.

[@luisangel1251]

Saved my day once again! Thanks!

[@darkwinter8]

I just finished going through the exact same problem as Example 1 for my homework, and I checked my solutions manual. The answers in the manual is 4(2xy + y^2)^3 - 3(x^2 + 2xy)t^2. I know what they're doing, but what happened to the "t" in the first half [4(2xy + y^2)^3)]? Or is that a typo?

[@penta4568]

bro you're my hero

[@mattman111123]

have you thought about investing in a document camera so its an overhead view instead of a slant? I'm sure you have probably made all the videos you need, but its just a thought :)

[@JohnSmith-bj7uc]

This video helped so much. Thanks man!

[@thimmyb]

This is awesome! Thank you for the effort! I kind'a feel guilty for not paying you.

[@tankmohit]

It's very helpful for me to understand backpropogation algorithm. That tree method is very similar to ANN.

[@yobhaji]

do you have a video on partial derivatives for implicit differentiation?

[@jiayunxiao509]

Ur videos are really helpful!!

[@altSt0rm]

Really useful and informative. Thank you!

[@applelacquio8862]

Youre such a BIG HELP! Thankyou! THANK YOU!!!!

[@linkmaster959]

For the last example, would it be wrong to back substitute the x and y function ? so the final answer is in terms of all u, v, and w variables?

[@martmelee]

Do you have any videos with optimization problems using partial derivatives? multiple variables calculus.

[@anonvingeta66ymous]

you have no idea how glad i am you exist dude :'|

[@Dusevic]

@patrickJMT must be. Thanks for the help!

[@brsznl]

why we used at 2:01 that symbol d to show derivative of t respect to x and why we used that symbol at 6:34 that seems d or (image of 6 in mirror) is there any diffrence between sayyin d or using that symbol?

[@floppyskater07]

Thank you very much man ! You are very good at explaining this!

[@msbijja]

PATRICKJMT FOR PRESIDENT!

[@ReWolWerKillZ]

+ili A Make Calculus Great Again

[@mariosv.8366]

Just a question... In the second example,if we suppose that y was only a function of v and w,and x remains a function of u,v,w. In this case how do we calculate dz/du? Im asking that cause by the chain rule we have to find the term dy/du,yet y does not depend on u...

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excellent...... superb, outstanding, magnificent, highest quality, of the highest standard, exceptional, marvelous,

[@skalaskanstefan]

very nice video , but if i may ask you something in the future.. Could you write your i's more like i's and not like j's , and the 2's more like 2's because it looks kind of like a Z. Can be confusing.. Otherwise thanks again for your videos, it really helped me. You're my savior ;)

[@NuncNuncNuncNunc]

Should the final expression have been expanded since x and y are functions of u?

[@chhasnat9539]

I wish you were my Multi variable Calculus Professor.