Implicit Differentiation

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  • Опубліковано 8 лют 2025
  • This calculus video tutorial provides a basic introduction into implicit differentiation. it explains how to find dy/dx and evaluate it at a point. It also explains how to find the slope of a curve given the x and y coordinates. In addition, it explains how to find d^2y/dx^2, the second derivative of the function using implicit differentiation. You need to be familiar with the product rule, chain rule, and quotient rule for derivatives.
    Derivatives - Free Formula Sheet:
    bit.ly/4dThzf1
    ______________________________
    Derivatives - Fast Review:
    • Calculus 1 - Derivatives
    Derivatives - The Product Rule - f*g:
    • Product Rule For Deriv...
    Derivatives - The Quotient Rule:
    • Quotient Rule For Deri...
    Derivatives - The Chain Rule:
    • Chain Rule For Finding...
    Derivatives - Composite Functions:
    • Derivatives of Composi...
    __________________________________
    Implicit Differentiation:
    • Implicit Differentiation
    Derivatives of Inverse Trig Functions:
    • Derivatives of Inverse...
    Derivatives of Exponential Functions:
    • Derivatives of Exponen...
    Derivatives of Logarithmic Functions:
    • Derivative of Logarith...
    Logarithmic Differentiation:
    • Introduction to Logari...
    ___________________________________
    Derivatives - Using Logarithms:
    • Finding Derivatives Us...
    Derivatives of Inverse Functions:
    • Derivatives of Inverse...
    Derivatives - Differentiation Rules:
    • Basic Differentiation ...
    Derivatives - Function Notations:
    • dy/dx, d/dx, and dy/dt...
    Derivatives - The Reciprocal Rule:
    • The Reciprocal Rule an...
    _________________________________
    Final Exams and Video Playlists:
    www.video-tuto...
    Full-Length Videos and Worksheets:
    / collections

КОМЕНТАРІ • 266

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Рік тому +34

    Derivatives - Free Formula Sheet: bit.ly/4dThzf1
    Final Exams and Video Playlists: www.video-tutor.net/
    Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
    Next Video: ua-cam.com/video/KbYW9FDm-Zk/v-deo.html

  • @sarak000
    @sarak000 4 роки тому +282

    I've spent days trying to get my brain to understand implicit differentiation. After dozens of videos from class and other youtubers, yours is the first one to have it make sense to me. Thank you so much!

  • @androidorb424
    @androidorb424 5 років тому +713

    You are the sole reason I am passing chemistry and calculus.

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    @alili86 3 роки тому +83

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    @christopherramsey6001 2 роки тому +2

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  • @ghb7860
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  • @axelevensen1517
    @axelevensen1517 3 роки тому +4

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  • @georgesadler7830
    @georgesadler7830 2 роки тому +4

    MR. Organic Chemistry Tutor, thank you for an excellent video/lecture on the classical Implicit Differentiation in Calculus I/II. This is an important topic in Mathematics and Engineering. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.

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    @murtuzahamayun9544 3 роки тому +10

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    @rashidissa5887 26 днів тому

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  • @j.o.5957
    @j.o.5957 2 роки тому +2

    It's so gooood, realizing that d/dx y^3 = d/dx * y^3/dy * dy = d/dx * 3y^2 * dy = 3y^2 dy/dx made my day

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    @edieberggren 11 місяців тому +1

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  • @stabme2005
    @stabme2005 4 роки тому +9

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    • @dkke825
      @dkke825 2 роки тому

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    @xbiohazardx7312 Рік тому +6

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  • @dong-wooklee
    @dong-wooklee 3 роки тому +40

    Shortcut for implicit differentiation
    Take all the things on one side
    then do as below:
    dy/dx= -(diffentiate wrt x, take y as a constant)/(differentiate wrt y, take x as a constant)
    Eg. Lets say I need to differentiate x³+3xy=y²+1
    Step1
    (taking everything on one side)
    x³+3xy-y²-1=0
    Step2
    differentiate x³+3xy-y²-1 wrt x and take y as a constant
    That would be equal to 3x²+3y
    Let 3x²+3y = m
    Step3
    differentiate x³+3xy-y²-1 wrt y and take x as a constant
    That would be equal to 3x-2y
    Let 3x -2y = n
    Step4
    Apply the rule and obtain dy/dx
    dy/dx = -m/n = -3x²-3y/3x-2y
    This may look like this is quite lengthy but in actual it hardly takes 10secs. I wrote this long so that anyone who sees this could clearly make sense of it and understand

    • @aooide
      @aooide 2 роки тому +1

      Interesting method, thanks.

    • @Maroofgilani621
      @Maroofgilani621 2 роки тому

      Thank you sir may I ask you a question

    • @Maroofgilani621
      @Maroofgilani621 2 роки тому

      7:23 how did -2x=cos xy² become y²cos xy² ??? Where did y² came from ???

    • @havagoodnight2724
      @havagoodnight2724 2 роки тому

      @@Maroofgilani621 he distributed cos(xy^2)

    • @drofeng
      @drofeng 2 роки тому

      @@Maroofgilani621 Chain rule : d/dx sin(u) where u = xy^2
      d/dx (sinu) = d/du (sin u). du/dx
      d/du (sin u) = cosu
      du/dx = y^2 + x.2y.dy/dx
      Then cos(xy^2) . (y^2 + x.2y.dy/dx)

  • @musumbaphesto687
    @musumbaphesto687 3 роки тому +3

    wow much love from uganda thanks for simpifying implicit differentiation for me

  • @ndngal143
    @ndngal143 11 місяців тому +1

    Thank you!!! this video just makes so much more sense than the textbook and class!

  • @umunnakenneth8111
    @umunnakenneth8111 3 роки тому +3

    Like Bro u r better than my text books and professors combined funny enough I didn't understand the rules but u also explained them...bro u r d best plsss keep it up😩❤

  • @joekerry2206
    @joekerry2206 4 місяці тому +1

    This gave me the key points needed to proceed with implicit differentiation.

  • @maddieschimanski8043
    @maddieschimanski8043 Рік тому +2

    i hope every side of your pillow is cold tonight you are single-handedly saving my calc grade ❤️

  • @carolinewright2078
    @carolinewright2078 2 роки тому +2

    Thank you so much, you just helped me a ton with my Math Econ homework!!

  • @gigachad3249
    @gigachad3249 3 роки тому +6

    Thank you, my teacher struggles to explain such basic concepts.

    • @dkke825
      @dkke825 2 роки тому

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  • @EliVang-v6q
    @EliVang-v6q Рік тому +5

    13:35 I believe you could have substituted 9 in for (y^3 + x^3) as well, thank you for the help!

  • @aaryanfootball9537
    @aaryanfootball9537 Рік тому +1

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  • @sparkled6547
    @sparkled6547 4 місяці тому

    my teacher sucks at teaching. I have been watching you for 3 years now so at htis point it doesnt matter if my teachers suck you help me pass anyways

  • @hassenfuad7258
    @hassenfuad7258 3 роки тому +6

    just came here to say thank you so much i just got 10/10 in calculus test.

  • @voodoochild24262
    @voodoochild24262 3 місяці тому +1

    gah i am so confused why we can use dy/dx = -x^2/y^2 in the quotient rule result but not for an immediate implicit differentiation of 3x^2 +3y^2(dy/dx) -----> 6x+6y(dy/dx)+3y^2(d2y/dx2)(dy/dx). it obviously doesn't seem to math out to the same answer....just feels weird that this doesn't also work
    you're the best as always!

  • @chelseaoliveira2962
    @chelseaoliveira2962 2 роки тому

    Thanks sm I was struggling so hard w/ this topic since my prof. didn't really go over it. You're a lifesaver, dude.

  • @zeyad3980
    @zeyad3980 4 роки тому +3

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    @allen.9 10 місяців тому +2

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    @travisjorgensen6734 2 роки тому +2

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  • @WhatIsTheHeat
    @WhatIsTheHeat Рік тому +3

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    @carlyjohnpillo6287 3 роки тому +1

    you help a lot dude i swear

  • @dreadhaisler6054
    @dreadhaisler6054 Рік тому +1

    12:56 To add, notice that y³ + x³ is also equal to our original given/expression x³ + y³, and it states that it is equal to 9. So subtituting the value of that expression will yield to a same answer. This is the beauty of second derivate in implicit, original expression tends to have a relationship on some part of it.

    • @nokuthulamakhunga7039
      @nokuthulamakhunga7039 Рік тому

      I have a question,so you mean second derivative will always give you the answer of the original equation if you substitute???

    • @dreadhaisler6054
      @dreadhaisler6054 Рік тому +3

      ​​@@nokuthulamakhunga7039 Actually, there are times that a given will not give you coordinates like (1,2) etc. But always remember that in implicit differentiation - second derivative, there's a higher chance that your solution will consist of the original given equation like for example here was x³ + y³ = 9, only the majority though, because some are not. Sometimes, you have to make little algebra tricks to make show of the original expression. For example, instead of getting y³ + x³, you get -y³ - x³, what you're going to here is to multiple it by "-" or -1, so it will become -(y³+x³) which will be equal to -(9) = -9.

    • @nokuthulamakhunga7039
      @nokuthulamakhunga7039 Рік тому

      @@dreadhaisler6054 thank you sir

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    @LP-rm6ek 5 років тому +9

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    @connorjacobsen5949 Рік тому +1

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  • @vford1000
    @vford1000 5 років тому +5

    Well explained and easy to understand, many thanks!

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    @yeeun2477 Рік тому +1

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    @Nkanyezii 2 роки тому +1

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    @oscarngan9970 5 років тому +1

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    @Aniqa-sn5ef 3 місяці тому

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  • @olz6928
    @olz6928 6 місяців тому

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    @aidenbailey6458 2 роки тому

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    @KatlehoMoeti 10 місяців тому

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    @MasiKarimi 2 роки тому +2

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    @alanflores5753 4 місяці тому

    My professor has the genius idea of starting with hard problem in this section...

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    @jsphcle Рік тому

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  • @3hustle
    @3hustle Рік тому

    0:01: ✏ Implicit differentiation is a method used to find the derivative of an equation with respect to x, by treating y as a function of x and adding dy/dx to every term containing y.
    4:31: 💡 The video explains how to use implicit differentiation to find the derivative of a function and evaluate it at a specific point.
    10:55: 📈 The video discusses finding the second derivative of a function using the quotient rule and evaluating it at a specific point.
    Recap by Tammy AI

  • @Gadonekoko
    @Gadonekoko 2 роки тому +1

    Thx for everything

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    @Fa25hass Рік тому

    best person on the planet earth

  • @mattmo8648
    @mattmo8648 2 роки тому +3

    I was totally following until you changed from dividing to distributing at abouit 6:48. I didn't track how the distribution worked.

    • @mattmo8648
      @mattmo8648 2 роки тому +1

      particularly when you distributed it to the derivated of xy^2. I don't see how the x ended up in the derivative of 1y^2, instead of it being 2y, or what happened to the 2y where it's x(2y(dy/dx))

  • @zackgrey4472
    @zackgrey4472 4 роки тому +10

    Does anyone understand why you add the (dy/dx) and how to know when to add it? I'm confused, how do you know when to put the extra differentiation

  • @thereishope651
    @thereishope651 5 років тому +3

    thank you for your videos.

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    @SerenaChoi-tr8fs 2 роки тому

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    @peteromocho2348 3 роки тому +1

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  • @omegachad7168
    @omegachad7168 Рік тому +9

    Dude my professor cant even explain this properly and If we have a question to ask he would just look at us like we are some dumb students and tell us its in the book. Like wtf????

  • @balllallalllalllallalhqbal2798
    @balllallalllalllallalhqbal2798 3 роки тому +7

    at 8:24 , could we cross cos(xy^2) in both numerator and denominator

    • @Th3Name
      @Th3Name Рік тому

      @toshio3772forgot about that, thanks for clearing it up

  • @ellieziska5961
    @ellieziska5961 2 роки тому +1

    Bro's casually saving lives

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    @aravindsai2409 3 роки тому +1

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    @but_is_it_art_6657 2 роки тому +1

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  • @shatteredknight1129
    @shatteredknight1129 5 років тому +15

    1:00 You don't really add the DY/DX. You times. But including it is a figure of speech. So it's a figurative add. But it will be taken literal and confuse users.

    • @codmlover6008
      @codmlover6008 5 років тому +2

      So I don't have to write it out on paper like that?

    • @diegoamorim7924
      @diegoamorim7924 4 роки тому +12

      @@codmlover6008 no you do, he just confused you by trying to clear up confusion, rip

  • @adrianmartin1394
    @adrianmartin1394 2 роки тому +1

    my poor brain. Still youre the best at explaining

  • @onion-brawlstars9792
    @onion-brawlstars9792 3 роки тому +2

    it would have been better if my text book had a link to this video

  • @alexanderrosen4574
    @alexanderrosen4574 2 роки тому +1

    thank you

  • @maybemaram
    @maybemaram 3 роки тому +1

    really saved me!!!

  • @nellielowe407
    @nellielowe407 3 роки тому

    You have helped me with so so many of your videos, and yet we don't even know your name :(

  • @comprehendnature2404
    @comprehendnature2404 3 роки тому +1

    As I understood it now, implicit differentiation is simply derivation with extra precision to what we are differentiating in respect of what. dy/dx. dr/dt. dv/dt ...etc. But normally d/dx is d to respect of X assumed and does not follow the rest of calculation.

    • @MrDarren690
      @MrDarren690 3 роки тому +1

      Yeah I think it attempts to relate y and x even though they’re visibly (in the equation) not in the regular y = x form. I keep hearing that it applies the chain rule, but if that were the case, then we’d need to treat y not as a single variable but as y(x) or a function of x. (Chain rule in y(x) 👉 would be y’(x) • x’.)

  • @hibaj4645
    @hibaj4645 Рік тому

    you are every student saver

  • @fatindewan27
    @fatindewan27 9 місяців тому +1

    I love you man

  • @urmyseed1907
    @urmyseed1907 3 роки тому +1

    Thank you🙏

  • @cemonycrissmiller9337
    @cemonycrissmiller9337 3 роки тому +2

    After this am probably passing my exam

  • @Opium41462
    @Opium41462 11 місяців тому

    once again very helpful

  • @mohanagreeshmagudhimalla1348
    @mohanagreeshmagudhimalla1348 3 роки тому +3

    at 2:14 would'nt it be -8/6 because it is dy/dx ?

    • @medicisounds1384
      @medicisounds1384 4 місяці тому

      Why in the living %^*# is there a negative placed there though

    • @safren4475
      @safren4475 2 місяці тому

      It's -x/y

  • @bigcrimsy
    @bigcrimsy 2 роки тому +1

    The thumbnail scared me with the -x^2/y^2 i thought everything i knew about derivatives was wrong lol

  • @naturalrelaxation3375
    @naturalrelaxation3375 4 роки тому +4

    8:22 , is it considered when you simplify the final answer by expanding it.?

  • @21mejia25
    @21mejia25 7 років тому +10

    at 7:36, can you explain how you got 2xycos(xy^2)dx/dy?

    • @gartyqam
      @gartyqam 5 років тому

      David Mejia
      if you dont know then ur dumb

    • @skillfulend0779
      @skillfulend0779 5 років тому +22

      @@gartyqam Respect yourself if were that smart you would have never came and watched this video in the first place.

    • @gartyqam
      @gartyqam 5 років тому

      @@skillfulend0779 who said i watched it i just came here cuz i know there are dumb people here and i just laugh at them

    • @josec2-b417
      @josec2-b417 5 років тому +5

      @@gartyqam You came here, therefore you just called yourself dumb, since you are among the "dumb people" here.

    • @AoShinden
      @AoShinden 5 років тому +4

      @@gartyqamyour edginess stings

  • @Maroofgilani621
    @Maroofgilani621 2 роки тому +2

    7:23 how did -2x=cos xy² become y²cos xy² ??? Where did y² came from ???

    • @hitmywoodsnyouchoke3113
      @hitmywoodsnyouchoke3113 2 роки тому +1

      He multiples the cos(xy2) into the 1y squared. He also multiples it into the other term that's being added in the parenthesis.

  • @Soranathpodcast
    @Soranathpodcast 6 місяців тому

    thanks for this lesson

  • @calebneher5623
    @calebneher5623 2 роки тому +2

    How do you know which terms have the dy/dx?

  • @hamadalmarzouqi2309
    @hamadalmarzouqi2309 4 роки тому +1

    I LOVE U MAN UR THE BEST

  • @EmmanuelOdarno-up2ej
    @EmmanuelOdarno-up2ej 9 місяців тому

    God bless you man 🙏🏽