Differentials and Derivatives - Local Linearization

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  • Опубліковано 4 лют 2025

КОМЕНТАРІ • 144

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Рік тому +6

    Derivative Applications - Free Formula Sheet: bit.ly/4eV6r1b
    Final Exams and Video Playlists: www.video-tutor.net/
    Calculus 1 Final Exam Review: ua-cam.com/video/WmBzmHru78w/v-deo.html
    Next Video: ua-cam.com/video/NL0NFV-O8Vg/v-deo.html

    • @heck6466
      @heck6466 Рік тому +1

      aye bro u the best

    • @tanwaduanhe7962
      @tanwaduanhe7962 Рік тому

      Hello Good sir, i was wondering of which one i should start watching on your playlists about Differential Equations. Hoping i would get a reply, thank you.

  • @yousifss3783
    @yousifss3783 5 років тому +168

    UA-cam University is the best LOL. I’m spending money to go college where they teach you nothing like that, everything is complicated but when I come to this channel I get what I want from the first example. Thanks a lot🙏.

    • @ghostfrom1950
      @ghostfrom1950 4 роки тому +6

      after getting my degree from Trump University, i'd have to disagree. Trump University trumps them all! LOL okay, bad joke. I actually do agree with your comment 👍

    • @raleigh2747
      @raleigh2747 4 роки тому +5

      Well one reason why this is free and your university is not is because sometimes the information here is misleading. dy/dx is not just a quotient ( as Leibniz thought it was) of the differential of y over the differential of x, because the differential of y is dependent on the differential of x. It so happens that following Leibinz's notation, it "appears" that you can do this but really, this violates the fact that in differential forms have to be independent of coordinates. The proof for why dy = f'(x)dx is not as simple as multiplying both sides by dx. Try solving the proof yourself or look up the work by Edwin Hewitt, Jerzy Łoś, and Abraham Robinson

    • @yousifss3783
      @yousifss3783 4 роки тому

      @@raleigh2747 Thanks for you explanation, I think we have an educational problems at the school, college or some book we use to learn or solve a problems, I have this question going on in my mind every time I learn something for example when my professor asks to answer a question about Maclaurin series, the issue is not really in how to solve the equations the Issue why I'm solving this what is the benefit, where I'm going to use it, give me a reason why I have to learn this not only coming to the class and wasting my time and you are not going to explain to me how the math you are teaching me is going to help me in my future. I have been asked this question by my classmates multiple times, and my answer was I don't know. And here when I started to look up every topics in what, where, when and how I'm going to use the math I learned in school. 🙂

    • @raleigh2747
      @raleigh2747 4 роки тому +2

      @@yousifss3783 I think the reason why teachers often don't say why a student is learning something is because the answer really wouldn't benefit the student. Take this as an example,
      Algebra student is learning about linear equations. Although linear equations have many applications, there really is no need to go soooo far in depth as algebra teachers do, it would seem. But the answer is really, algebra students learn about linear equations for two reasons, it easily demonstrated the basic concepts of algebra, but really, its so that when they take calculus, its so that they understand tangent lines, and linear approximation and their proofs. But think about it, if a student asked, "why are we learning so much about lines?" and the teacher told it like it is, "so that you understand tangent lines, and linear approximation and their proofs in calc." the student would go uhh... okay, with no real increase to their motivation to learn it.
      unfortunately, in math, sometimes you gotta learn it with no real understanding of why you are learning it at the time. The understanding will come later.

    • @yousifss3783
      @yousifss3783 4 роки тому

      @@raleigh2747 Yes for sure specially when you finished calculus and you think I finished calculus, but you realized no Static, Electric and Dynamic etc, are bringing me back to where I started which is algebra, for me I deal with equations as puzzle to solve and it is quite fun, for some students no I don't want to deal with math. I mean yes I struggle and when I struggle and I don't easily give up I keep search the information on the internet because. But no one wants to search or try. They want someone to feed them calculus which is what I'm doing right now with some students who are seeking for help, but they don't realize that I was struggling like them one time and asking the same questions and whenever they ask me I just say you have special tool called internet use it and everytime you feel like that you forgot something go back to your notes or to the internet.

  • @superbutter476
    @superbutter476 4 роки тому +405

    When a 10 minute video beats your whole week of class

    • @somekindofname7859
      @somekindofname7859 4 роки тому +1

      Yes

    • @raleigh2747
      @raleigh2747 4 роки тому +8

      Well one reason why this is free and your university is not is because sometimes the information here is misleading. dy/dx is not just a quotient ( as Leibniz thought it was) of the differential of y over the differential of x, because the differential of y is dependent on the differential of x. It so happens that following Leibinz's notation, it "appears" that you can do this but really, this violates the fact that in differential forms have to be independent of coordinates. The proof for why dy = f'(x)dx is not as simple as multiplying both sides by dx. Try solving the proof yourself or look up the work by Edwin Hewitt, Jerzy Łoś, and Abraham Robinson

    • @petergriffon8520
      @petergriffon8520 4 роки тому

      @@raleigh2747 can you use this and solve every question correctly?

    • @raleigh2747
      @raleigh2747 4 роки тому +3

      @@petergriffon8520 depends on what “correctly” means. If change in x is sufficiently small, then the approximation will be close to the actual value of f(x) at the point. However, if you are looking for an exact answer, finding differential equations by “multiplying” change in x to both sides will not work, especially when there are more variables.

    • @itsCraftedPvP
      @itsCraftedPvP 3 роки тому

      @Asa Harley or its a scam that actually hcks ur account

  • @beepsheep5954
    @beepsheep5954 3 роки тому +32

    This is the hardest part of calculus fck differential. I'm amazed to those people that can understand this.

    • @MuhammadBilal-f4f
      @MuhammadBilal-f4f 10 місяців тому +2

      couldn't agree more it sucks
      Nobody's explaining the intuition too, they are just throwing already proven facts

    • @bpavankumar9597
      @bpavankumar9597 10 місяців тому

      ​@@MuhammadBilal-f4fwatch professor Leonard's video for differential in calc 3 playlist.

    • @coldshock5181
      @coldshock5181 9 місяців тому +1

      ​@@MuhammadBilal-f4fwhat do u find hard about it?

  • @xtv_
    @xtv_ 5 років тому +41

    Thank you so much! 1 example here explained the 2 hours of lecture from my professor. God bless!!!

  • @eduardovaldez7830
    @eduardovaldez7830 5 років тому +66

    Bro i have an exam in 2 days, u are a literal blessing to us humans.

  • @alexandrestamkos7488
    @alexandrestamkos7488 2 роки тому +3

    My boy right here is the TOP G of calculus. Man I love you

  • @Hypnotic.-.
    @Hypnotic.-. Рік тому +6

    I’m in precalc and I watched this for fun lol I know it gets harder but you made it seem so easy. I understood all of it and was able to do your examples on my own. I wish you were a teacher in my high school 😂

  • @ExpungedFunkyFriday
    @ExpungedFunkyFriday Рік тому +1

    This guy explains Soo good that I literally understanded everything in the first minute

  • @mariosspyrou1054
    @mariosspyrou1054 5 років тому +111

    The videos from 2006 are very good

  • @jbonceu2457
    @jbonceu2457 2 роки тому +4

    Its crazy how all of this relates to primarily understanding the SLOPE which we all learn in algebra 1. Slope is change in y/change in x. dy just means change in y, dx is change in x. Derivative (dy/dx) then means we are finding the slope of the equation.

  • @andrewsciencetube3828
    @andrewsciencetube3828 4 роки тому +9

    all videos on this channel are what I need to understand. I hope in the next few days I can be equal with my high school teacher by using this tutorial as the main helper.

    • @raleigh2747
      @raleigh2747 4 роки тому

      Unfortunately you wont be "equal' with your high school teacher because dy/dx is not just a quotient of the differential of y over the differential of x, because the differential of y is dependent on the differential of x. I'm sure your teacher knows this. It so happens that following Leibinz's notation, it "appears" that you can do this but really, this violates the fact that in differential forms have to be independent of coordinates. The proof for why dy = f'(x)dx is not as simple as multiplying both sides by dx. If you want to be equal, try solving the proof yourself or look up the work by Edwin Hewitt, Jerzy Łoś, and Abraham Robinson

    • @andrewsciencetube3828
      @andrewsciencetube3828 4 роки тому

      @@raleigh2747 ok maybe you are right so i should correct my word " i can go adequately....." but you have to always remember that there are some students beyond their school teacher. because when you have a real interest in math you will read more and more than even your teacher.

    • @elladre137
      @elladre137 Рік тому

      Did you surpass your teacher?

  • @saddamkasumo927
    @saddamkasumo927 3 роки тому +4

    You are the best thing to ever happen to us .. I have an exam in 2 minutes 😃

  • @mangalover8764
    @mangalover8764 4 роки тому +12

    Thank you so much!
    You're our hope in passing calculus especially this time of pandemic

  • @jalisabroussard8245
    @jalisabroussard8245 4 роки тому +33

    Hi, your videos are extremely helpful. Is there a way you could record with higher audio volume? I always struggle to hear your audio clearly and turn my volume up all the way.

    • @eljefea2802
      @eljefea2802 3 роки тому +4

      Buy another pair of headphones.

    • @BarnesWelding0609
      @BarnesWelding0609 2 роки тому

      You may also be able amplify it through your devices bluetooth settings. Or the speakers settings

    • @BluesB0x
      @BluesB0x 2 роки тому +2

      @@eljefea2802 lol not helpful. what kind of headphones? if op were to invest in better headphones, like you vaguely suggest, it would be even quieter due to a likely higher power draw. A DAW or amplifier would be much more helpful and actually increase the volume ;)

  • @MacdonaldNkhoma-vo5gx
    @MacdonaldNkhoma-vo5gx 9 місяців тому

    You really don't spend your time for nothing we are benefiting a lot from your services❤❤🎉

  • @cynical-q2y
    @cynical-q2y 16 днів тому

    I came up with a thought. The way we can see dy and dx as two terms rather than dy/dx for the entireness is actually showing the accuracy of calculus when it approaches to calculate the instaneous change. When dx approach infinitely small, we should be able to predict the change(dy=delta y) though we will never know how exact small it will be. It is kind of the coherency of the theory, but still intuitively.

  • @georgesadler7830
    @georgesadler7830 Рік тому

    Professor Organic Chemistry Tutor, thank you for a short and awesome video/lecture on Differentials and Derivatives in Calculus One. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.

  • @simpleinformationhub8553
    @simpleinformationhub8553 2 роки тому +1

    Good job I always found your videos when I searched.

  • @ian-hm6cx
    @ian-hm6cx 3 роки тому +4

    this guy deserves a space in heaven specially reserved to him

  • @FataIIity
    @FataIIity 2 роки тому

    I have a midterm in a week with no idea how to do anything and now its 2am and here I am watching organic chemistry tutor

  • @shivanielitem6533
    @shivanielitem6533 5 років тому +2

    You help me survive my math class everyday, Thank You So Much!

  • @aylinmachaen7536
    @aylinmachaen7536 3 місяці тому +1

    thank you i love you

  • @argie5697
    @argie5697 4 роки тому

    Fuck it.Coz of ur wizardness, i also recommended you to my friends and classmates who struggled a lot in mathematical subjects such as Calculus. Everything I am looking for is in your channel, that's why when i search something, i always look for The Organic Chemistry Tutor having a black background number thumbnail.
    Thanks a lot, youre helping me pass this smester. Youre really a big help specially this time that we are set to new normal. Youre my teacher, not my online modules. heartheart

  • @guliyevshahriyar
    @guliyevshahriyar Рік тому

    Thank you very much for precious content

  • @mallninja9805
    @mallninja9805 9 місяців тому +1

    What does "the differential" mean. "...and dx = 1/4" - why? What does it _mean_ to set dx = 1/4? Where does it come from? Is it something you can graph? WHAT DOES IT MEAN?

  • @nylesnguyen9336
    @nylesnguyen9336 4 місяці тому

    this is flipping awesome

  • @abdelrahmane657
    @abdelrahmane657 2 роки тому

    Totally agree with Super Butter’s comments. 👏👍🎓

  • @ayeshaafzal4884
    @ayeshaafzal4884 3 роки тому

    This is hands down too good

  • @zachh6868
    @zachh6868 4 роки тому +2

    How can a 10 minute video teach better than a 40 minute video lecture?

  • @abdulsalamolayemi9388
    @abdulsalamolayemi9388 Рік тому

    Please I need a video on first principle differentiation

  • @zoCalesterio-cq1yq
    @zoCalesterio-cq1yq 2 місяці тому

    just a question teach, on 4:01 on the given equation 54-24+8 your answer was 38, however if we apply the pemdas rule it is 22 through which addition is made first before subtraction, am i wrong or what haha kindly address my question. thank you.

  • @zulaikhabatool3467
    @zulaikhabatool3467 2 роки тому

    So much helpful video 📸

  • @chriswilliams5291
    @chriswilliams5291 Рік тому

    So delta y and dy are similar values when delta x is small but grow further apart as delta x becomes a bigger value? Are delta x and delta y used for applied mathematics in the same way that derivatives are?

  • @hanadiyousif5637
    @hanadiyousif5637 2 роки тому +1

    In 1:51 how did you find that 3x

  • @platypusih8u830
    @platypusih8u830 8 місяців тому

    kinda confused, what is the difference between dx and delta x? what is delta exactly (talking about the triangle one not the delta-epsilon)

  • @mohammadamiw
    @mohammadamiw 2 роки тому

    It was really good ❤ thanks 🙏🏻

  • @XxHXRxX
    @XxHXRxX 4 роки тому

    I've learned one thing. The proximity of a result, compared to what's understood is acceptable.

  • @arashfrz4053
    @arashfrz4053 Рік тому

    God bless you❤

  • @GaSLAPENnu
    @GaSLAPENnu 17 днів тому

    Finally understood it

  • @BangMaster96
    @BangMaster96 5 років тому +1

    But, delta x -> 0, wouldn't dy = 0 then, because you multiply the derivative by delta x ?

    • @raleigh2747
      @raleigh2747 4 роки тому +1

      Yes exactly, this is one reason why dy/dx is not just a quotient of the differential of y over the differential of x, because the differential of y is dependent on the differential of x. It so happens that following Leibinz's notation, it "appears" that you can do this but really, this violates the fact that in differential forms have to be independent of coordinates. The proof for why dy = f'(x)dx is not as simple as multiplying both sides by dx. Try solving the proof yourself or look up the work by Edwin Hewitt, Jerzy Łoś, and Abraham Robinson

  • @phamhuutri1996
    @phamhuutri1996 4 роки тому +1

    so what is the difference between derivative and differential ? i am getting mixed up between them

    • @kristeldempseydeguzman8
      @kristeldempseydeguzman8 4 роки тому +2

      DERIVATIVE of a function is the rate of change of the output value with respect to its input value, whereas DIFFERENTIAL is the actual change of function (got these info from google)

    • @Boog1137
      @Boog1137 4 роки тому +2

      In the scope of this section, you could think of the whole derivative as the term dy/dx and the differentials are the individual dy and dx seperately

    • @tutstorial8474
      @tutstorial8474 4 роки тому

      but isn't it dy/dx not a fraction ?
      but why does it becomes dy bg just multiplying dx to the equation?

  • @TheNightmare150
    @TheNightmare150 3 роки тому

    I have a question: What happens when you got dy=xdx and u pick x=0 and dx=1. Theoretically delta y shouldn't be 0 but in this case it would be. Or am I getting something wrong?

    • @shreycrescent
      @shreycrescent 3 роки тому

      you could i would assume take x=1 and dx=-1

  • @tutstorial8474
    @tutstorial8474 4 роки тому +1

    i thought dy/dx isn't a Fraction??

  • @ShiroKage-h8v
    @ShiroKage-h8v Рік тому

    so what if like y=x+5ycos(2x)

  • @tristankarlmalala9702
    @tristankarlmalala9702 3 місяці тому

    my exam is later at 730am, right now its 130am , im cooked

  • @princyshilshi8480
    @princyshilshi8480 Рік тому

    Why can't teachers explain like this

  • @god8511
    @god8511 5 місяців тому

    What does the number 0.1 in dx=0.1 represent someone help please

  • @ahmadal-khaldi2663
    @ahmadal-khaldi2663 3 роки тому

    How come I get 3.33333 when I put 1/2*Sqrt9 times 0.02 in the calculator, as seen in the last example

    • @Hypnotic.-.
      @Hypnotic.-. Рік тому

      2 years later but uh 1/2(sqrt(9)) is equal to 1/6 and then multiply that by 0.02 and you get some number idk

  • @telutron9755
    @telutron9755 4 роки тому

    Amazing sir

  • @zakariya5460
    @zakariya5460 3 роки тому

    this is so easy

  • @ukjfx
    @ukjfx 3 роки тому

    Thank you 😊

  • @ثابت-ج6ض
    @ثابت-ج6ض 3 роки тому

    good math thanx

  • @ThatDrummerFrank
    @ThatDrummerFrank 6 років тому +4

    I have never seen a differential be assigned a numerical value before. In all of calc I, II, III and diff eq. Are you sure this is okay to do? Usually dx, dy, danything represents an infinitesimally small change in whatever value the differential is. Where did you learn this? If it's mathematically legal, then it's news to me.

    • @ericfarmer5715
      @ericfarmer5715 5 років тому

      Dx is the differential of x and it is mathematically equivalent to the change of x or delta x for some interval (x, x+ delta x ) the differential of x and delta x are equal dx= delta x

    • @coep_leader4898
      @coep_leader4898 5 років тому

      I agree- delta x and delta y is the notation for finite increments

    • @ipodtouch470
      @ipodtouch470 5 років тому

      As far as I know this only works for local linearization were Delta x = dx and Dy aprox = dy

    • @sevrothegoblin5212
      @sevrothegoblin5212 5 років тому

      When assigning dx to a value it is a representation of linear approximation

    • @mryup6100
      @mryup6100 5 років тому

      I know that for sure it is illegal mathematically in some areas.

  • @Amir4v
    @Amir4v 2 роки тому

    oh my god
    thank you very much
    wow :)

  • @hanmaVS
    @hanmaVS 7 місяців тому

    I come here for explanation about derivatives and differentials but instead I've got 10 minutes video where guy solves some problem, why

  • @airplanefood6121
    @airplanefood6121 4 роки тому

    thanks

  • @ume6864
    @ume6864 3 роки тому

    Whatvis the meaning of it

  • @comicsconerr
    @comicsconerr 2 роки тому

    Thank you have an exam in 20 min

  • @ytman-lq2mj
    @ytman-lq2mj 5 місяців тому

    Nice

  • @ardenburns1719
    @ardenburns1719 3 роки тому

    wow, i wish we had learned this earlier, it makes alot more since this way. only thing that im confused about now is when to use dy/dx or just dy?

  • @babrakazizi5878
    @babrakazizi5878 6 років тому +5

    What is dy and dx?

    • @deathrider365
      @deathrider365 6 років тому

      Dy and dx is dy/dx split up. You multiply dx to get out from below dy. It is implicit differentiation

    • @iboa6938
      @iboa6938 5 років тому +1

      @@deathrider365 so it's like f(x) and g(x)? I never heard of dy/dx ?

    • @risalia7638
      @risalia7638 5 років тому +1

      ibo a no, dy/dx is just the notation you use when you differentiate something. It can also be written as f’(x), for example. However, as you advance in calculus you tend to use dy/dx a lot more and ditch the other notation to manipulate your derivatives for problems such as these.

    • @raleigh2747
      @raleigh2747 4 роки тому

      @@deathrider365 dy/dx is not just a quotient ( as Leibniz thought it was) of the differential of y over the differential of x, because the differential of y is dependent on the differential of x. It so happens that following Leibinz's notation, it "appears" that you can do this but really, this violates the fact that in differential forms have to be independent of coordinates. The proof for why dy = f'(x)dx is not as simple as multiplying both sides by dx. Try solving the proof yourself or look up the work by Edwin Hewitt, Jerzy Łoś, and Abraham Robinson

  • @jtak
    @jtak 5 років тому +1

    thank u for ur videos! please speak a little bit louder though :" sometimes i have to turn your vids to the highest max

  • @zhandoshumyrbek9814
    @zhandoshumyrbek9814 3 роки тому

    5:44

  • @BrotherIntel
    @BrotherIntel 4 роки тому +2

    My exam is in 9 hours LOL

  • @asrafialmamun5767
    @asrafialmamun5767 Рік тому

    Wrong explanation in deriving differential.
    First you differentiate " lnx" w.r to x.
    Thant means dy/dx=1/x
    After that you multiplied both sides by dx and here is the wrong explanation you've done.
    Here d/dx is differential operator which is not a fraction. So you can never multiply both sides by dx.
    Please give the correct explanation.

  • @Jawahir-l5u
    @Jawahir-l5u 2 роки тому

    💛💛💛

  • @cyvenfx7271
    @cyvenfx7271 3 роки тому

    What the hell that's so much easier

  • @Jawahir-l5u
    @Jawahir-l5u 2 роки тому

    💛💛💛💛💛💛💛💛

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    @Jawahir-l5u 2 роки тому

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  • @sebastiangiray3614
    @sebastiangiray3614 4 роки тому

    Compute
    dy and Δy for y=ln(x^2+1) as x changes from -2 to -2.1. can someone help me? coz when i solve delta Y i cant punch my calculator ln(-2.1) - ln(-2) because it gives math error... hope some one can help me pls coz i cant sleep without figuring this shit out XD

  • @PardeepSingh-jh6ou
    @PardeepSingh-jh6ou 5 років тому

    Square root of 0.037

    • @jesusc0der
      @jesusc0der Рік тому

      0.192353840617 Approximately.

  • @tibeihahowillis5836
    @tibeihahowillis5836 3 роки тому

    Does anyone else feel complete when he taps his calculator

  • @arvinbm6243
    @arvinbm6243 4 роки тому

    Hmmm...

  • @maryrosesaldua7107
    @maryrosesaldua7107 3 роки тому

    Smooooth

  • @myst5454
    @myst5454 4 роки тому

    But what the fuck does dy mean? I get how to find it but what does it meannnn

  • @justusfrimpong809
    @justusfrimpong809 5 років тому

    Godbless

  • @杨滢-j9c
    @杨滢-j9c Рік тому

    甚至让我一个英语口语一般的人听懂了。。。

  • @sarahjaneimad7103
    @sarahjaneimad7103 2 роки тому

    Je suis nul en math

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    @Jawahir-l5u 2 роки тому

    💛💛💛💛💛💛

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    @Jawahir-l5u 2 роки тому

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    @Jawahir-l5u 2 роки тому

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    @Jawahir-l5u 2 роки тому

    💛💛💛💛💛💛

  • @Jawahir-l5u
    @Jawahir-l5u 2 роки тому

    💛💛💛💛💛💛