❖ Implicit Differentiation ❖

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  • Опубликовано: 16 ноя 2024
  • 📚 Implicit Differentiation: Basic Idea and Examples 🧮
    In this video, I discuss the basic idea behind implicit differentiation, a crucial technique in calculus for finding derivatives of implicitly defined functions. We’ll cover the essential notation and mechanics, along with some foundational concepts to help you understand this important topic.
    🚀 What you’ll learn:
    The difference between explicitly defined functions and implicitly defined functions, with examples to illustrate each.
    How to apply implicit differentiation step-by-step, recognizing that when we take the derivative with respect to x of a function of y, we are treating y as a function of x.
    Insights into how this process essentially utilizes the Chain Rule.
    A couple of worked-out examples to reinforce your understanding and demonstrate the application of implicit differentiation in practice.
    Whether you’re new to calculus or looking to refine your skills, this video is designed to provide clarity and confidence in using implicit differentiation.
    Don’t forget to check out my other videos for more insights into calculus, derivatives, and advanced mathematical concepts!
    👍 Like, subscribe, and hit the notification bell for more educational content! 🔔✨
    Watch now to master the basics of implicit differentiation and enhance your calculus skills!
    #ImplicitDifferentiation #Calculus #MathTutorial #LearningMath #ChainRule #Derivatives #MathConcepts #EducationalContent #STEM #Mathematics #MathHelp #CalculusExamples #DerivativeTechniques #FunctionNotation #APCalculus

Комментарии • 788

  • @curtishaley3606
    @curtishaley3606 9 лет назад +134

    Why are you so much better than my teacher

  • @SpartanSPI
    @SpartanSPI 9 лет назад +42

    Tried khan academy. There wasnt a step to step, in depth explanation of where d/dx and dy/dx came from. All of the info seemed jumbled and mixed, and thus unclear. I never comment on videos but you explained this so well i just have to say thank you, well done.

    • @sohaibbaig248
      @sohaibbaig248 9 лет назад +5

      gotta agree, this is a rare topic on which khan failed to help me.

    • @RepTheKingJC
      @RepTheKingJC 6 лет назад

      a Khan Academy isn’t really that great when it comes to math.

    • @ujuuju4311
      @ujuuju4311 4 года назад

      for me khan focuses on conceptualizing the subject that sometimes i cant understand what he's saying lol, i learn and understand math through bunch of practice where i get from patrick and organic chemistry tutor.

    • @Nathaneal51
      @Nathaneal51 4 года назад

      @@ujuuju4311 u need to have a conceptualised understanding of what your doing, otherwise youre just a robot churning out numbers

    • @ujuuju4311
      @ujuuju4311 4 года назад

      Yeah that's true what I mean Is that i understand those concept through some bunch of practice problems because Khan usually explain things in just one example which is not enough for me

  • @numba1spazzet
    @numba1spazzet 9 лет назад +74

    Thank you so much! You don't know how much i've been struggling in calc this semester. Literally, while watching this i felt teary eyes by awe because i finally understood something. THANK YOU!!

    • @patrickjmt
      @patrickjmt  9 лет назад +19

      glad it helped! i have quite a few examples on this if you need to see more

    • @harrymax8072
      @harrymax8072 9 лет назад +2

      patrickJMT You got me through last year man. Powerful patrick JMT.

    • @sokoloko5108
      @sokoloko5108 9 лет назад

      +patrickJMT big thank from me too. My teacher didnt show me that. Thank you so much!!

    • @nylahrenee
      @nylahrenee 8 лет назад

      Literally same here lol. It really helped A LOT.

    • @draculiciouscoffinlove7122
      @draculiciouscoffinlove7122 8 лет назад +1

      his other videos are great too

  • @ashleymonahan8299
    @ashleymonahan8299 10 лет назад +77

    I can't thank you enough for this. After days of struggling with this I finally have SOMETHING down. Thank you!!!! This is your calling, I hope you do it for a long time. :)

  • @thenozar7603
    @thenozar7603 8 лет назад +17

    As a lefty I admire your ability to not drag all the ink around the paper.

  • @mathnerdm
    @mathnerdm 8 лет назад +11

    Words can't explain how incredible your videos are. Your teaching style of just jumping straight into examples is exactly how I learn best, and I can't thank you enough!

  • @makennammm
    @makennammm 12 лет назад

    I have had multiple teachers, TA's, and tutors try and explain this to me... your video was so much clearer than any of their explanations. Thank you so much!!!

  • @syd_jzx100
    @syd_jzx100 8 лет назад

    It's 2016 and you're still saving lives. Thanks man, absolute legend.

  • @Johnny.deeeeeep
    @Johnny.deeeeeep 10 лет назад +11

    You have my everlasting gratitude sir

  • @seanmcdougall3212
    @seanmcdougall3212 11 лет назад

    PatrickJMT, I've been trying to get someone to explain this to me all day, and 4 people couldn't get it through to me. You broke it down barney style, and got me in the right direction in 7:06. It's not perfect yet, but I'm on the right track. Thanks so much for all you do.

  • @sebastianbroncano7643
    @sebastianbroncano7643 7 лет назад +21

    Studypug: Are those videos from 2006 really helping??
    Me: Yes they are. Thank you Patrick

  • @BunnyHanyou
    @BunnyHanyou 12 лет назад

    Oh my god. I almost cried as my calc prof was teaching this. It was so confusing, I thought I for sure was doomed. May god bless you sir! You are a LIFE SAVER.

  • @biscaynebuckets
    @biscaynebuckets 9 лет назад +66

    And my teacher got me thinking this is some sort of rocket science! lol Thanks Pat

  • @aishwaryax333
    @aishwaryax333 12 лет назад

    YOU ARE AWESOME. I've been struggling with implicit for forever and my teacher doesn't help at all... but you just made it soooo much easier to understand!

  • @dapianna23
    @dapianna23 4 года назад

    I've been struggling with implicit differentiation for months in calc and 2 minutes in and it all makes sense. You're a God send. Thank you

  • @mtech1020
    @mtech1020 13 лет назад

    you are the idol of my entire calculus class. we worship you

  • @dmsfid7205
    @dmsfid7205 15 лет назад

    There is no other person who knows how to explain tricky things like this and turn it into an easy one. Thank you for All your video!

  • @whatsername131313
    @whatsername131313 14 лет назад

    It helps a lot more to see examples worked out by a person and explained rather than just reading from a textbook. Thank you so much for your commitment to free education on the internet, I'm sure you have helped many maths students

  • @brendanj5419
    @brendanj5419 11 лет назад

    I learn more from you in under ten minutes than i do in my 90 minute classes. Thanks Patrick.

  • @ikecharles7071
    @ikecharles7071 10 лет назад +40

    OH MY GOD. This is it?? My teacher made this so darn difficult! Wow man I appreciate this so much!

    • @akinkunmiayo4219
      @akinkunmiayo4219 10 лет назад

      My teacher did the same too.When its so freakking easy. ^_^

  • @pringlelays159
    @pringlelays159 8 лет назад +10

    This guy is helping me a ton on ap calc

  • @Ramyfication
    @Ramyfication 12 лет назад

    Thanks for all these videos Patrick. My UNIVERSITY professor sent an email to our class with a link to your website which just goes to show how undeniably good your videos are. Keep up the outstanding work!

  • @designer72hd41
    @designer72hd41 7 лет назад

    You made reading a textbook to learn mew material so much easier to explain and show step by step process. Thanks Patrick!

  • @TheFasian
    @TheFasian 12 лет назад

    Thank you so much, this was confusing me because other websites never explained what was going on or used strange notation, but you made it so clear and simple.

  • @platinumisgr8
    @platinumisgr8 12 лет назад

    i really hope you are a highly paid professor at MIT or something, i can understand more and learn 10x as much on a 7 minute video from you then i an in 2 hour classes. thank you so much

  • @Dug1423
    @Dug1423 11 лет назад

    Ive been following your vids throughout my calc classes and this one by far has helped me the most, my prof explained this in such a complex way and I was so lost, this makes so much more sense now, thanks!!

  • @sllrsm
    @sllrsm 11 лет назад

    Makes it sooo much easier for my calculus final this week. Gatta give you the thanks for using your time to help others.

  • @MrOmaralamri
    @MrOmaralamri 10 лет назад +5

    i have an exam tomorrow and you just gave me the biggest favor ..
    thank you sooooooo much Mr

  • @Luckyxseven
    @Luckyxseven 13 лет назад

    You sir are amazing, I don't understand why professors can't just teach it the way you just did...

  • @Stooeybear13
    @Stooeybear13 13 лет назад

    Incredible. Opened up my original notes for my maths course at uni and didnt make any sense to me, your video cured my fear of implicit differentiation. Thanks alot!

  • @steveszymczak448
    @steveszymczak448 10 лет назад

    I had one professor who could do a lesson this quickly and effectively. the only difference was since it was a classroom settings he stopped for questions and also did progressively harder examples but this style is just so much more effective it cuts out all the bs. I don't even pay attention in my current lecture class because this teaches me the way I learn: straight to the point no bs.

  • @BboyRagnar0us
    @BboyRagnar0us 9 лет назад

    The problem with the teachers is that, they take you around, confusing you more and more and never get to the point straight away! However, with your calm voice and simple teaching you made me understand a lot more than i ever hoped to understand! If you have more of these, and perhaps a more advance level of these exists that i'll be taught in the following semester, please share them! Thank you very much!

  • @DavoC17
    @DavoC17 13 лет назад

    omg dude,
    your explanation on this and the chain rule is superb,
    you literally explain all the jargon surrounding the notation which is usually my biggest confusion, thanks heaps!

  • @TreasureGodsCreation
    @TreasureGodsCreation 10 лет назад +41

    Watching this for my Calc Finals tomorrow. (:

    • @ZuestTV
      @ZuestTV 9 лет назад +3

      ***** idk why they teach us physics...its useless for a programmer >.

    • @Baby19901990
      @Baby19901990 6 лет назад +1

      im saying the same thing but 3 years later.

    • @prakhar_rides_away
      @prakhar_rides_away 6 лет назад

      ZuestTV so that you can program software/firmwares in machines (like construction machines, cars, aeroplanes etc etc etc)

    • @brandonchristophermccartne1079
      @brandonchristophermccartne1079 6 лет назад

      got a test in 90 min lmao

    • @moonladd4083
      @moonladd4083 5 лет назад

      @@Baby19901990 I'm saying the same thing but now 1 year later.

  • @maggiekong8681
    @maggiekong8681 11 лет назад

    you are AMAZING. I was struggling with calculus and you were recommended from our teacher, and you have helped me so much you have no idea. Thank You!!

  • @paigehausladen1520
    @paigehausladen1520 9 лет назад

    Study for first calculus final of my semester in college/first semester of senior year because I'm a PSEO student and this video is such is such a big help! Thank you so much 😊

  • @braveheart4lif31
    @braveheart4lif31 12 лет назад

    didnt understand this from weeks of lecture, watched 6 and a half minutes of this video and it hit me like a brick wall at 60 mph, thank you so much.

  • @jenn9580
    @jenn9580 15 лет назад

    Thank you so much. I have learned more from your videos than I have learned in the last 2 semesters of Calculus & Differential Equations.

  • @jeveuxlesoleil
    @jeveuxlesoleil 14 лет назад

    We were talking about you in my calculus tutorial a few days ago. Everyone passed their gateway exams = definitely as a result of these videos.

  • @AnnLaustsen87
    @AnnLaustsen87 12 лет назад

    Who knew I'd be re-learning implicit diff for linear algebra? Your videos along with Paul's notes have helped me get back on track after being out of calculus for 5 years. Thanks so much!

  • @stephanymainea1271
    @stephanymainea1271 10 лет назад +9

    I understood this better in your 7 minute video than in my hour long calculus lecture. THANK YOU!

    • @TheGaara802
      @TheGaara802 10 лет назад +2

      ur lucky it is only an hour, my lecture is 2hrs long of crap

    • @patrickjmt
      @patrickjmt  10 лет назад +3

      very happy to help ;)

    • @joannaperez051
      @joannaperez051 10 лет назад +1

      ***** Same here. -_-

  • @TBVorzy
    @TBVorzy 11 лет назад

    Thank you so much! My professor taught this a completely different way, but this is so much easier to understand. The night before a test I always just sit down and watch every video you've made about anything that will be on the test and it helps so much!

  • @reonai7145
    @reonai7145 8 лет назад

    You make it so easy to understand. You are a large reason why I'm actively passing calculus.

  • @fleabagx34
    @fleabagx34 10 лет назад +2

    That whooped the ass of a 55 minute lecture any day of the week!

  • @rodneymuleya9540
    @rodneymuleya9540 9 лет назад +5

    patrickJMT YOU ARE THE WORLD'S GREATEST MATHS TEACHER, YOU ARE MATHEMATICALLY GIFTED

  • @wobblycogsyt
    @wobblycogsyt 11 лет назад

    Excellent video, really explains the concept well. I particularly like the fact that you chose a non-trivial example to show us as well.

  • @Laconicer
    @Laconicer 12 лет назад

    Whenever I am lost in my calculus class, I tell myself Patrick will solve everything. And I was never disappinted. (: Thanks so much.

  • @goku63forrealzzz
    @goku63forrealzzz 7 лет назад

    the way you write is so satisfying. I already covered this topic before, and came here to revise, everything clicked like a flash, but I stayed just because how satisfying it was. Thanks anyway, and keep up the great work :)

  • @GoodiTwoShuz
    @GoodiTwoShuz 12 лет назад

    Patrick you explain in 3 minutes what my teacher does in one period. That's 'nuff infotainment for me :)

  • @tupacsomething69
    @tupacsomething69 13 лет назад

    u deserve the nobel prize in teaching, they should create this category just for u

  • @TheLmhampton
    @TheLmhampton 13 лет назад

    Thanks. This helped quite a bit. Like others, I'd normally figure it out using the text but my text this semester is bad enough that even my instructor said it stinks. You've cleared up one of the things that's had me virtually pulling my hair out in confusion.

  • @kneine15
    @kneine15 13 лет назад

    wow.... ur 7 min and 6 sec video beats my professor explaining for 2, 3 class. THANKS!!!!

  • @iantrankinful
    @iantrankinful 13 лет назад

    This completely cleared up confusion about dy/dx. My prof wasn't explaining it at all. Thank you so much!

  • @angcientrock
    @angcientrock 11 лет назад

    I totally agree with Jethro. I'd say your youtube popularity also gives great incentive for publishers' interest in something like that. Or maybe a dvd that includes problem sets for each section. Math is awesome!

  • @kenyaaroxursox13
    @kenyaaroxursox13 12 лет назад

    PATRICK JMT!!! REPLACING ALL MATH PROFESSORS!!! GOD BLESS YOUR SOUL!

  • @chipuarbuu
    @chipuarbuu 12 лет назад

    Yay! :D Clarity!!!! I've been failing all my tests, quizzes and homework, but let's hope I can comeback with your video help!

  • @Artyfil
    @Artyfil 15 лет назад

    THANK YOU!!! I'm using this to study for my calculus midterm and you sir have helped me learn in 7 minutes what I've been trying to learn in the classroom for a couple weeks now lol.

  • @Whitebunny00
    @Whitebunny00 11 лет назад

    OMG thank you.. this is so helpful! I am taking an online calc class and I could NOT understand it from reading the textbook... you explain this so well!

  • @logancarras1154
    @logancarras1154 5 лет назад

    It's my junior year and im in BC Calc; when we got to this section, I was just totally lost. But now, I actually understand it! I wont fail the test now! Thank you so much for all you do; you, sir, have earned a sub.

  • @Elusefelier
    @Elusefelier 15 лет назад

    You win, good sir. Thank you for these videos . There is huge value in explaining things in a simple way - it's so much easier to understand everything!

  • @WaterboyVe
    @WaterboyVe 10 лет назад +1

    Thank you soooo much!!!!! You have made derivatives soooo easy for me!!! You have to be the best teacher hands down for math!!! You make complete sense, you're clear, and you explain each step throughout the examples. Again, thank you!!!

  • @TaylorBogle
    @TaylorBogle 13 лет назад

    Thanks so much! You make this so much easier for me to understand than my calc teacher, and he talks for 90 minutes on stuff like this. Lol. Needless to say, I really appreciate your videos.

  • @user-ym1su1vn2l
    @user-ym1su1vn2l 9 лет назад

    Thank you!!!! studying Physics BSc with open uni, seriously got stuck on this..... Now ive watched this its so simple, explained in a way my books somehow could not convey.

  • @adavid21
    @adavid21 14 лет назад

    Patrick is the best at simplification of the concept. I wish he was my teacher! Thank you sooo much for your contribution to the math world!!!

  • @josepaul2000
    @josepaul2000 11 лет назад

    If only I had your voice running in my head during my exams.. Things would magically seem so much clearer!

  • @Hypersc0re
    @Hypersc0re 3 года назад

    This video is almost 12 years old but I'm so happy I found it. Thanks for the amazing explanations!

  • @littlemissmurderer21
    @littlemissmurderer21 9 лет назад

    Your videos are REALLY helpful! I have a calculus final tomorrow and this video helped me understand something that had been impossible for me all semester! Thank you so much for posting videos, I truly appreciate it and you're a great teacher!

  • @accel103
    @accel103 12 лет назад

    i feel like i could learn more from you in a week than i could from calculus teacher in a semester

  • @pbjLUBESTER
    @pbjLUBESTER 12 лет назад

    you sir, are a gentlemen and a scholar, and are saving my GPA this semester

  • @antoinepelletier1182
    @antoinepelletier1182 12 лет назад

    My teacher fails so much explaining this, I wonder where he got his PhD! Probably not in teaching! He is a very good mathematician but BOY he teaches like everyone was on his level, which makes the class uncomprehensible!
    I LOVE YOUR VIDEOS!!!!!!!!

  • @iloveihop07
    @iloveihop07 12 лет назад

    this is definitely one of your best videos, implicit differentiation can be a beast sometimes

  • @silverbot01
    @silverbot01 14 лет назад

    Amazing, ive been looking for a good explanation for implicit differentiation for a week now. I can't believe I found it here on youtube! Thank you very much!

  • @Skit10daddoleSucker
    @Skit10daddoleSucker 11 лет назад +1

    YOU EXPLAINED SO GOOD!!! WAY BETTER THAN MY TEACHER WAS OVER THINKING THE PROCESS UNTIL NOW THANK YOU SO MUCH

  • @lovelyanimeangel
    @lovelyanimeangel 13 лет назад

    You are a math math GOD!! Thanks to you, I was able to understand this, and I'm totally prepared for my Calculus finals tomorrow!

  • @ginwithair
    @ginwithair 12 лет назад

    THANKS! GREAT TO HAVE YOU AROUND SIR!

  • @sibityuiop
    @sibityuiop 13 лет назад

    I would just like to say a VERY BIG THANK YOU TO YOU! I hope you live for over a 100 years!

  • @seaorshore
    @seaorshore 10 лет назад +6

    YOU MAKE EVERYTHING MAKE SENSE!

  • @1randomchikk
    @1randomchikk 12 лет назад

    I know people thank you often for your help and you probably hear this a lot but I would just love to say THANK YOU SOOOO MUCH~! once again because you honestly just like made this concept so much easier to undersand! I love that when I dont understand somethingin class I could always come to you and then I get it!!

  • @bodybuilder718
    @bodybuilder718 13 лет назад

    Men and Women everywhere spread the word!!!!!!! i pay good money for a professor that can barely speak English and can not teach worth a damn! my advice, do not listen at all in class, just write the topics and look at these videos! might seem extreme but my A in calculus 2 is proof that this man can make the toughest things look so easy, thanks Patrick you are the man! 8 people that disliked this failed cal just before seeing these videos!

  • @Rid4ayomi
    @Rid4ayomi 9 лет назад

    Imagine the world without PatrickJMT, omg u're such a big helper in students life !!! Thanks!!

  • @zakriayounis718
    @zakriayounis718 9 лет назад

    you are the only one getting me through first year engineering bro, love your videos

  • @RyanPMcGowan
    @RyanPMcGowan 13 лет назад

    You and KahnAcademy are saving me this semester. Generally I learn from the same book that my homework is from, but the book this semester is... bad.
    Thank you.

  • @DrSickShots
    @DrSickShots 11 лет назад +1

    I love your videos. 7 minutes sum up everything, whereas the book talks about all kinds of crap to get to this idea. Saving me lots of time, for more exercises !

  • @mthuddleston
    @mthuddleston 11 лет назад

    Man it's frustrating when the ThatTutorGuy ad pops up. PatrickJMT has my heart (Also my A in Calc 1 and B+ in Calc 2!) Thanks :)

  • @gennnnnnnnnn
    @gennnnnnnnnn 11 лет назад

    Thanks for your help =)
    Went into Calc 3 after taking a break from math for 2+ years and I was totally lost, lol.
    But now, I see the light!

  • @TheMaxinoob
    @TheMaxinoob 11 лет назад

    THanks so much once again, Patrick. Not only you helped me to ace my provincial exam and u are motivating me in excelling in calculus

  • @OrejaBeja
    @OrejaBeja 12 лет назад

    I'm crying right now. I FINALLY understand it! THANK YOU SO SO MUCH!!

  • @arnarfreyrkristinsson8650
    @arnarfreyrkristinsson8650 6 лет назад +1

    Thank you! You made my day, I was struggling with this for hours and finally got it

  • @sportsstar20062006
    @sportsstar20062006 10 лет назад

    You're seriously the best! I learned more in this example than in three hour long lectures

  • @1955stefanie
    @1955stefanie 12 лет назад

    OMG! I was suffering because if that implicit differentiation, and you explained it so well, I feel great! (and the sun is shining! )

  • @114Freesoul
    @114Freesoul 12 лет назад +1

    I missed my class on this, thanks for getting me back in line!

  • @thoyo
    @thoyo 11 лет назад

    once again i join the multitude in thanking you for taking my professor's place. good on ya ;)

  • @Nick-wp7nm
    @Nick-wp7nm 11 лет назад

    Your videos are why I might pass my calc class. Thanks man.

  • @feelikefoxtrot
    @feelikefoxtrot 13 лет назад

    I had no idea until i watched this. You are my hero.

  • @Wizerik299
    @Wizerik299 11 лет назад

    This taught me better about implicit differentiation in 7 minutes than my professor did over the course of 3, 75 minute classes. :D

  • @reelfilm13
    @reelfilm13 14 лет назад

    it's funny...in high school I was watching your videos on how to do limits, and I am in college now watching your videos to explain implicit differentiation---thanks so much for the help

  • @MultiWarbird
    @MultiWarbird 8 лет назад +4

    You're the best man on this planet. Patrick for president 2016!!!

  • @Ultisymo
    @Ultisymo 12 лет назад

    Love watching calculus videos on youtube, it's so much easier to understand!

  • @snowflake89100
    @snowflake89100 12 лет назад

    Thank you, sir, for making everything so simple and easy.

  • @RyanStarcraftProtoss
    @RyanStarcraftProtoss 13 лет назад

    @patrickJMT omg, you are 5x better at explaining this than my teacher. she just tells us how to do it, not why you do it.