Implicit Differentiation

We are pretty good at taking derivatives now, but we usually take derivatives of functions that are in terms of a single variable. What if we have x's and y's in there? We need a new technique! It's called implicit differentiation, and it goes like this.
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[@RemixerUltimate]

Multiple days of class and it just wasn't clicking. And it takes one 10 minute video to cement it. Holy hell.

[@bennybickerton2149]

Who needs school when big dog Dave is on the job haha

[@muffy4671]

New response just dropped

[@stephaniemangwiro6301]

Thank you so much, who knew you could learn more from an 11 minute KZbin video than a 45 minute lecture

[@__lunareclipse]

Pretty Much

[@brandonzarate2736]

Yeah you can learn from an 11 minute video. Although keep in mind, you can also pause the video and re-watch parts that did not make sense the first time around. Also the videos are tailored in the fashion where he's teaching to you directly in front of you. In lecture, you may be sitting far from the professor making it difficult to hear and see. Also, here in the video he just goes over the steps. Sure, there are moments where he explains why some things are the way they are which is helpful but not in the same sense as in the lecture. Lectures from math professors cover more than how to do problems. They cover the reasons why more in depth. I"m sure if student went to their professor's office hours and asked how to do the certain problems, they would similar results to watching this video. Sorry if I appeared to be attacking you. I didn't mean this directly at you and I get the feeling you were just saying it general.

[@anishreddyanam8617]

Dude same

[@zuhaib_meo_rajput]

Thnk you Sir, after getting this video; this time, I am able to do exercise my self. Love U from PakistaN

[@deringthomas5363]

You guys have lectures?

[@chocolateylovv8792]

ive never understood this concept for almost a year and my exam is tomorrow, the moment i understood i almost cried tears of joy, thank you so much!!!

[@jamesmakau4992]

what a crap

[@dewgantuah1815]

😂

[@dewgantuah1815]

😂

[@iknowyoucanhearme6483]

I can somehow relate to that tears of joy. The feeling where you no longer have to be scared because you already know how to attack the problem.

[@pratikshadutta7843]

I am also watching the video a day before my exam. Tomorrow is my exam 🤧

[@MrJuandahero]

I hate to admit it but the color coding the breaking down each step made this crystal clear. Here, have an thumbs up

[@frostbitepokin9520]

I hate to admit but red reminds me of period blood

[@E_Rico]

Why would u hate to admit that?

[@santi044]

Why would u hate to admit that

[@ivoryas1696]

@@E_Rico He probably thinks it would make him seem simpler-minded, possibly not knowing that's how many people study.

[@ivoryas1696]

@@frostbitepokin9520 Hate to admit it, but that reminds me of period bacon.

[@ramithjayasuriya]

its 1AM and i'm getting ready to the exam tomorrow. and didnt know a thing about this, but this video made me understand every possible way it could happen. Thank you so much.

[@sinioofficialposer4311]

Ramith Jayasuriya we're the same bro, I've got an exam Tomorrow and still don't have an idea how what is in implicit Differentiation, a big thanks to this video tutorial

[@ramithjayasuriya]

Pabutaya Ando good luck buddy!

[@lolamoon7296]

Ramith Jayasuriya *Same here, a high school senior filled with regrets for taking Ap Calculus*

[@winner1338]

Did you pass the exam?

[@julianjoseph5033]

Do you mean today since it’s 1AM?

[@eigentheory]

I have seen this video many, many times and I must say it is hands down the best explanation of implicit differentiation that I have seen. I hope to use this explanation when I am able to teach Calculus one day!

[@golembes]

I am a calculus teacher and I have looked a few videos on this subject. Your video is the first one I have watched that actually does this mathematically correctly. Thank you! If students simply memorize a process and do not understand what is happening, they are going down a dead end street. Your video was very easy to follow and you emphasized quite nicely the concept of "the derivative of something with respect to something else" - a critical concept as we progress through calculus. It is not about getting the right answer it is about getting the right answer by understanding the mathematics. Thank you! I will post your video for my students in addition to my own videos.

[@undeadman7676]

I'm currently taking Calculus 1 from home without any video lessons or instructions from my professor because of the current pandemic. This video has gotten me a perfect score on my assignment that is due in 2 days. I understood it well enough to even take it to its second derivative, and that's from a single 12 minute video. I'm excited to go back and work through the proofs for this for a few days once I finish my exam!

[@arrtwo1375]

Got a calc test tomorrow and this is saving my ass. Thanks dude.

[@tahmidadib4018]

Man calc gives me goosebumps

[@8DJYash]

How did it go

[@kels8823]

This was the first video I found that actually explains WHY things are happening with implicit differentiation, specifically, around the 3:00 min mark. It is also the clearest visual representation, much easier to follow than someone hand writing at a whiteboard. Also, you are just low key encouraging, so thanks! I appreciate your efforts!

[@635atom]

I agree. I'm currently taking Calc 1 in college, and my professor never explained why we keep dy/dx. I have no clue why it's apparently so uncommon to teach why this is happening, but I appreciate this guy's videos.

[@erniemyleskeelerkeeler]

You someone give this guy a Nobel prize. I could listen to a lecture all day, come home and learn 5 times as much watching a small video. thank you Professor Dave, Keep up the fantastic work

[@HappyRhino]

I'm sure you get an increase in views during finals- and its well-deserved! Thanks for the refresher.

[@Justin-ne6rw]

mine is next week

[@evanmastermind]

3:30am; test tomorrow. Finally learning this stuff.

[@Iucebowel]

Studying at 1:00 AM, got a math test tomorrow and this helped a lot; Thank you!

[@connerbills7892]

Dave could probably teach me to perform brain surgery in an afternoon. This man is goated.

[@treymtz]

I've taken cal like 2 times now. This is the one video that made implicit differentiation understandable.

[@astro_boi27]

I'm going to a 100-item calculus exam tomorrow guys pray 4me💪❤

[@violethill4454]

how did it went

[@astro_boi27]

@@violethill4454 I got a passing score!! (65/100, passing is 60)

[@astro_boi27]

@@violethill4454 I passed! (barely)

[@Tom-vk2rv]

@@violethill4454i think he died

[@woopwoop2601]

I just came across this for the first time, having somehow missed it in my previous university modules, and I swear that you're the only person who managed to make this seem like the simple concept that it is. I came across Khan Academy's explanation first, and they made such a song and dance of it I was lost within 5 minutes xd

[@meepter1542]

I just rewatched the Khan Academy videos and did the practice but I was so lost too. Once I watched this I was like "ohhh, makes complete sense." I'm glad I'm not the only one haha.

[@7betty]

No one can teach like this in the whole youtube community you are the best professor the world had ever seen

[@artemis_719]

holy cow i literally cannot thank you enough. Didn't take me until watching this that i understood and just got a perfect score over the quiz I took today on this concept. You explain it literally perfectly. Thank you 😭

[@lindaslele6561]

You explains best..we like it great explanation...

[@felixkuadugah9108]

Yup

[@slek_cs]

Not gonna lie, I need to pay more respect to X 😂

[@cheskaoliveros8227]

This is the only tutorial video I'd really appreciate.. Now I understand the implicit differentiation very well.

[@andriskirsis8401]

Professor should have just shown this video in class. Thanks. I haven't understood this at all until watching the video.

[@johnahmirlawas7854]

If teachers and instructors would teach like this then contents like these on yt will never would have been existed. So props to them for making yt math video tutorials so great.

[@WarriorX16]

We are doing partial derivatives in Calc 3 and had to do implicit differentiation as well. This definitely helped refresh my memory, thank you.

[@ankitdhaka]

Thanks!

[@sondidu]

I'm here because my teacher can't teach

[@lekissdarams7195]

Same here bro 😭

[@x-90]

This stuff is too hard

[@NgaxVEVO]

Than that is not a teacher

[@Islamaroma1919]

Me too

[@jackyboyvods7852]

same

[@Re-nq2uh]

Thank you so much! I'm a 12th grade student who studies alone without the help of any teacher, i cannot thank you enough for it. You and other great youtubers are helping me a lot with my studying i really appreciate you

[@puddleduck1405]

good luckkk!!

[@Re-nq2uh]

@@puddleduck1405 thank youu

[@maxchan105]

Very detailed and clear explanation with no steps skipped. Helped me to understand a lot! *Silencely curse my teacher which skips all the steps when he is explaining this theory - confuse me

[@mhonthungovung7122]

Very clear voice and can easily understandable, thank you so much for giving such a wonderful and easy examples..

[@margot9303]

Words cant express my gratitude for Professor Dave.....

[@asdgautam1476]

Thank you for the awesome explanation,it helped clear my doubts substantially.If you ever read this,I have a few suggestions- 1.Could you try bringing more complex problems in your lectures,as they seem very basic to me rn. 2.I think there is a mistake in the 2nd answer at 11:00 ,the correct answer should be (5y-2x)/(6y-5x) Other than that,the lecture was awesome,and you truly deserve my sub.Looking forward to clear more doubts through this channel! With love from India.

[@Adityagarg0]

For 2. Multiply both numerator and denominator by -1 answer will be same

[@asdgautam1476]

@@Adityagarg0 oh yeah,mb

[@nullFoo]

This explained it SO much better than my textbook, thank you!

[@s3n1ch]

Thank you man! I have understood much better than from my analysis teacher from Universitatea Politehnica Bucuresti, Romania! :)

[@alisageyl]

thank you so much!! as a gratitude, i will never skip any ads on your videos. please continue uploading videos it really helps us!

[@ProfessorDaveExplains]

I'll never stop! Oh and if you feel like clicking an ad, even better, that's how I get paid :)

[@alisageyl]

@@ProfessorDaveExplains im a civil engineering student and your channel really helps me understand the fundamentals. okayy i will click your ads if that helps!

[@evansonndungu6054]

For business students, your lecture ends at 8:44

[@PokeShadow77]

Gah you lucky business majors!!!

[@Luingus]

thank you! im teaching myself calculus and you helped my grasp this topic after struggling for days!

[@defytyrantsofmississippi2198]

That’s awesome! I’m teaching myself calculus as well.

[@ifonlytherewasmoretime187]

Your video came in clutch for my math final, thanks so much you're better than my teacher by far lol!

[@MohamedRabe33]

Thank you I have learned a lot from you ,from Egypt 🇪🇬

[@rzjnbtg1546]

my teacher taught us the first part and usually i wouldnt get any part of it but your vid hits me very easily after 4 minutes and i was able to solve it independently

[@minatlasanimaisha3816]

I was so worried bcz I couldn't find the type that our professor taught. But thanks a lot you uploaded a video exactly same style that our professor taught, all of my confusions are gone now. A bunch of thanks. If I could like this video a million times, I would do that.

[@lethilethuy3891]

this is the best explanation on youtube thank you

[@neutro1538]

Thank you soooo much, I've been trying to wrap my head around this topic for ages, thinking of y like a function of x was a godsend, thank you sir :)

[@hoshicakes3]

I've watched so many videos about this topic but this is the only one that made sense to me. Hats off to you sir, you got my eternal appreciation

[@pauldalnoky6055]

I've seen a dozen videos on implicit differentiation. This is the best.

[@VylaNwale]

I love you professor Dave❣️

[@jacobshoup]

Professor Dave once again saves my ass just in time for my test

[@Shineyourlightwithglory]

This video is explicit, 5 years ago,yet it is still building strong minds. Well done Prof. Dave❤

[@fatenzaf9782]

this 11.45 minutes video worth my 6 month of learning implicit differentation at my school lol

[@9308323]

*11.7333...

[@user-hj1fk4mh7d]

it’s 💯 true. Prof Dave is an infinite times better than my prof such that my prof will never reach prof dave’s level of teaching.

[@arulmc7733]

I am a 9th grader with a great interest on quantum physics and general mathematics. Your explanations are really great and user friendly that, with your lectures anyone can understand anything. I also greatly admire your vids on quantum’s and modern physics. Please continue these works with more interesting concepts. All the best.

[@gartyqam]

@@Safwan.Hossain you can teach a 6 year old to do calculus. however, they don't know what it means

[@HeckYeahRyan]

where are you now?

[@nickchylinski5878]

was looking for a professor dave video to put on in the background while doing calc homework, and as it turns out, professor dave can actually help me with my homework XD

[@yuannie269]

im gonna subscribe because this channel will be my survivor for college

[@beans7285]

I did not expect it to be the product rule. After understanding that, it became much easier. Thanks m8

[@TheNamesFathom]

I've been watching your channel for the debunks for months now, never thought I'd be using it for the calc explanations too!

[@anorak_2902]

Ok this video was actually incredible you allowed me a 10th grade algebra 2 student with some basic knowledge of derivatives actually understand implicit differentiation.

[@petermorgan5645]

Outstanding video. Cleared up all my issues with the topic in one go. Thanks!

[@domdubz7037]

I appreciate the content and think you do a good job presenting the material. However, I’d really appreciate much more complex rigorous examples using multiple derivative rules in one problem.

[@veronicagong9106]

Going to have the ib finals 2 days later, huge thanks to professor dave for saving my maths

[@keshavraj1389]

What is ib

[@jxrr.]

Never understood this topic but thanks to u, i know how to do it now

[@primeprime1047]

11:00 i find a different result for the second questionn. I'm differenciating myself right now. Anyway, thanks a lot it helped me so much even though i studie math in french at scool.

[@barrydavis331]

Hi, I got 5y-2x for the numerator.

[@cosmicpsyops4529]

Let me guess, you are here because your professor didn't cover this enough in Calc I? Thanks Professor Dave! You set the bar for explaining this. And those small pauses in between sentences...critical for encoding and integrating this material with preexisting calculus code.

[@ianbell9041]

Thank you. Although this video did not explain everything I needed- you provided enough detail for me to easily solve for (dy/dx)y which helped me understand where y' comes from. Honestly I think that notation is extremely confusing when mixed with dy/dx. Anyways, I appreciate you. Good luck to everyone else taking calculus currently.

[@Reachnopreach]

Hey Dave, I was kinda struggling wrapping my noodle around this one, but you explained it really well. Kudos!

[@Since-dy4rt]

Thank you soooo much for making this video!! Class lecture and other KZbin videos did not make sense to me but now I finally get it I could cry lol

[@mehakmalik31]

You made it so easy... Thanks a lot

[@hareecionelson5875]

Professor dave, you're a legend and for extra fun, implicit differentiation of y=arcsin(x) produces the time dilation formula of special relativity if x= v/c

[@ZeeLord7]

Thank you , I appreciate your effort,

[@niturampuria9019]

Couldn't thank you more! Brilliant explanation

[@JulieWu-q3f]

Best ever explanation for implicit differentiation!!

[@sleepyitgirl]

Thanks for your clear and short explanation! Appreciate for it!

[@manikdas1429]

Thanks i just needed this

[@rafurafu9645]

very well explained. this video is very helpful. thanks a lot good sir, may the gods take your soul to Valhalla

[@celinewest1250]

Incredibly helpful, thank you!!

[@29928]

thanks for making my life super clear before the exam!

[@MrHavoc313]

Thank you for making this video, so much clearer now

[@ByiachOnFire]

You taught me more in 11 mins than my teacher did in two 1.5hr class

[@barrydavis331]

You make the best videos! For the 2nd problem at the end (11:00), I got 5y - 2x for the numerator.

[@teddyplanet]

Same! I got (5y-2x)/(6y-5x)

[@guidopierdomenico5108]

@@teddyplanet same, can someone explain

[@savagegamer290]

@@guidopierdomenico5108 If you multiply both numerator and denominator by -1, you will get the same answer in the video

[@mariakhan6090]

Professor Dave is the Maths, Science, and Chemistry Jesus!

[@mattk6182]

did not know you were such an accomplished pianist, I switched from a degree in violin performance at FSU to statistics, lets jam !!

[@krishaashvsingh6811]

Thank you so much for clearing this heavy concept in just 11 minutes

[@hwillis7570]

Thanks, nice work and clear explanations.

[@sofieooms8990]

wow this was really good, thank you

[@fireflies15]

this is an incredible explanation. thank you very much

[@whoopietv9678]

Thank you very much professor dave.😁

[@Ricky02]

Starting is entertaining

[@08patboy]

ty you've explained it much better than my lecturer

[@helenabaker5275]

thank you so much!!! this video was amazing and i feel so much better about implicit differentiation! you are the best!!!! :)

[@SamnissArandeen]

I was understanding this course up until you started swapping back and forth between Y and f(x), just saying that d/dx y^2 was composite without clearly showing why, and eventually after so many times trying to rewatch this one, I had to give up and ask a friend to explain this to me.

[@yaboiidave2255]

saving my grade once again with an clear explanation and great examples, thanks again Prof!

[@insert6190]

This video really helped me out with the more complex ones thanks

[@Tetelowh_munchies]

I managed to understand implicit differentiation in only 11 minutes but I spent an hour an half in my lecture hall and i didn't even understand a thing.

[@trinhham328]

Finally able to understand this... Thank you so much, clear and so helpful.

[@imlilj5x]

had a quiz n watched this video 5 mins before which broke the concept down perfectly

[@MisterH1992]

It's 3:41am and I randomly decided to watch knowing very well I understand implicit differentiation.

[@rafiaimranbts8369]

Thankyou so much tomorrow is my exam and this video proved very helpful

[@ivoryas1696]

Just a question, if anyone's up to answer. In that last problem, I honestly can't tell were the cosine went. I _definitely_ need to review my trig at some point, but I thought I had a pretty good handle on it and this just isn't checking out to me.

[@ishantkatal5538]

Thanks for a such a trick ... I m ready for give a exam tomorrow

[@JiggyWasTaken]

You are such a life saver Dave, thank you.