Derivatives of Composite Functions - Chain Rule, Product & Quotient Rule

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  • Опубликовано: 25 ноя 2024

Комментарии • 200

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  10 месяцев назад +4

    Derivatives - Free Formula Sheet: bit.ly/4dThzf1
    Final Exams and Video Playlists: www.video-tutor.net/

  • @butyrate
    @butyrate 3 года назад +234

    Honestly don’t know what I would do without this RUclips channel

  • @traviswells6938
    @traviswells6938 2 года назад +61

    i swear this guy could just do every teacher on earth's job without a sweat. He's honestly one of the biggest reasons im passing maths.

    • @talolsen8513
      @talolsen8513 Год назад +1

      european person eh. glad to see you doing well brotha.

  • @T3chAnalogy
    @T3chAnalogy 3 года назад +53

    Hello everyone coming back to review for midterms. I wish you luck on your weary travels.
    Edit: Also thank you for all your hard work and dedication to teach anyone willing to look up your videos. Greatly appreciated!

    • @Happypotato917
      @Happypotato917 9 месяцев назад

      How can I when you belong to me but I belong to them

    • @verudoralast4890
      @verudoralast4890 6 месяцев назад

      Erm what the sigma

  • @yaxchegacus9182
    @yaxchegacus9182 2 года назад +6

    39:48 Y=[5+4x]^4 [7x-x^2]^5 is a product and chain rule combined but, you mistakenly said product and quotient rule hope this will clarify the misunderstanding to future people watching this. great youtube channel to learn Math and Science

    • @dekeijzergeorge9974
      @dekeijzergeorge9974 8 месяцев назад +1

      yeah i wa like wtff is going on im i hearing right 😅

  • @brentsrx7
    @brentsrx7 2 года назад +6

    This content is changing the career trajectory of hundreds of thousands of people, thanks.

  • @POJ
    @POJ 5 лет назад +105

    Watching this 00:36 am
    Edit 1: this is 3 years later and i love how i still get comments from my late night chemistry homies. Also i finished chemistry at the same time this comment went up and im not looking back good luck to anyone having chem exams.

  • @carlsondsouza
    @carlsondsouza 3 года назад +77

    Hi ,
    At 51:55 f prime of 1 is -3 so the end result is 34/4 = 17/2 i.e. 8.5

    • @simonlameck6359
      @simonlameck6359 3 года назад +10

      Exactly, but he has done a great job explaining derivatives.

    • @Eblt3
      @Eblt3 2 года назад +2

      Thank you!

  • @JasonVaysberg
    @JasonVaysberg 3 года назад +91

    At 37:01 you forgot to carry down that the tan function was squared, so the answer should be 30xtan^2(5x^2+8)*sec^2(5x^2+8)

    • @winsoronate8046
      @winsoronate8046 2 года назад +2

      Yah itx squared he 4got

    • @rediet3703
      @rediet3703 2 года назад +3

      ya I was confused I thought I got it wrong but..

  • @carina-fz5pd
    @carina-fz5pd 4 года назад +185

    Just wanna say thank you for all of your videos! You are saving my life in calc during quarantine :) literally learn more in an hour of your videos than I do in a week of classes :0

  • @patricklynch9145
    @patricklynch9145 3 года назад +7

    You just explained this way better than the Princeton Review book did. The book has good practice problems I just find it hard to understand their explanations. Thank you so much 🙏

  • @LeBronthemvpboss6
    @LeBronthemvpboss6 3 года назад +47

    Watching all of your calc videos before my 2 quizzes and test. Hopefully, I'll do well.

  • @mythicalcat6292
    @mythicalcat6292 6 лет назад +22

    Shows all the types of questions seen in AP tests great job

  • @seokjinniesluv
    @seokjinniesluv 3 года назад +8

    heard this channel from my classmates and this first video i watched is pretty informative. i now know why they all learned the lesson fast 😩

  • @mahibehulu2045
    @mahibehulu2045 2 года назад +4

    you are the teacher who every student wants thank you very much.

  • @thedevourerofgods1686
    @thedevourerofgods1686 2 года назад +17

    I have an indescribable desire to learn things above my grade level (as of writing im in 9th) and i cant begin to tell you how good this video is. You are very good at writing it all out so if i make an error i see exactly where it was, along with a cohesive and understandable explanation

    • @VerdantSeeker
      @VerdantSeeker Год назад +4

      im proud of u (: never let this intellectual curiosity fade-it will carry you through life

    • @kaad-ku8jf
      @kaad-ku8jf Год назад +1

      nice pfp

    • @AbhiramMylavarapu
      @AbhiramMylavarapu Год назад +1

      Same bro, even I am in 9th grade and I am learning calc to be ahead everyone!!! If I start now, I won't face much problem in the future

  • @KundanYadav-ds9hl
    @KundanYadav-ds9hl 2 года назад +19

    composite function starts from 18:13

  • @robintuition4164
    @robintuition4164 5 лет назад +44

    chain rule 18:00

  • @villetons7071
    @villetons7071 Год назад +1

    Thanks for this channel, it's a great help for someone who has plan to take board exam

  • @juan15car
    @juan15car 3 года назад +20

    Very Nice Video
    The only I want to say that at 51:55
    You put 2(3) where it supposed to be 2(-3) in which will change your answer from -6+40/4 which is then equal 34/4 which is then equal to 8.5

    • @abdulazizalfarsi6967
      @abdulazizalfarsi6967 2 года назад +1

      I wanted to comment about this point also.

    • @dawnmyke2161
      @dawnmyke2161 2 года назад

      Sharp observation there. I also got it 8.5 (34/4). Nonetheless, Great kudos to the TUTOR of TUTORS!

  • @moseskiprono8594
    @moseskiprono8594 Год назад +1

    This channel has made me a saviour to my fellow students

  • @lauralove1119
    @lauralove1119 2 года назад +4

    I can't believe I made it to the end of this video but I did. This was so helpful and I took notes on everything. The exam is next week wish me luck!

  • @kopiladhakal1560
    @kopiladhakal1560 Год назад

    I wouldn’t even try to dream about being a doctor without this guy 😢

  • @adinathreghunandan6484
    @adinathreghunandan6484 3 года назад +1

    This guy is an absolute hero at teaching

  • @kamilamohamed284
    @kamilamohamed284 2 года назад +6

    52:01 you forget f’(1) is not 3 it is actually -3
    And the answer is 34/4

  • @McFlashh
    @McFlashh Год назад

    The way this guy talks is nice and soothing

  • @arslanahmad5500
    @arslanahmad5500 2 года назад +1

    i really respect of you sir,you are very inteligent person you provide us knowledge with full detailed and dont miss any point
    love you sir

  • @skylersoltesz9608
    @skylersoltesz9608 2 года назад +1

    I have my final tomorrow, thanks for clutching up for me. You my guy

  • @dailyshadow
    @dailyshadow 4 года назад +9

    This is really helpful. Thank you. Commenting just to help the algorithm.

  • @uba_Michael10
    @uba_Michael10 3 года назад +3

    If i had sarted from childhood with the oct videos I would be very brilliant but anyways his videos has transformed my academic life in the university. I don't know how to thank u so much oct

  • @theperipateticaccrescent7685
    @theperipateticaccrescent7685 4 года назад +2

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  • @smartdean8910
    @smartdean8910 2 года назад +1

    This Good. I thought we were gonna factorization that quadratic

  • @gianmarcrosario3288
    @gianmarcrosario3288 Год назад +2

    I think the answer of tan³(5x²+8) should be 30xsec²(5x²+8)[tan(5x²+8)]², correct me if I'm wrong.

  • @zoyakaira4422
    @zoyakaira4422 2 года назад

    Thank you ( this channel) for existing.

  • @yxtung6719
    @yxtung6719 Год назад +1

    for 37:06 , tan(5x^2 + 8 )should have square , tan^2(5x^2 +8) :D

  • @uba_Michael10
    @uba_Michael10 3 года назад +4

    Pls I would love u to upload hyperbolic derivatives cos u are my only reliable source of learning 😔 plsss

  • @fmt55
    @fmt55 2 года назад +1

    Thank u for all the vids they are the best help and explanations in the world👍

  • @violetgallegos3594
    @violetgallegos3594 2 года назад

    thank u, thank u, thank u you´ve lit saved my career , my mental stability and other stuff haha you´re the senior of calculus thanks again

  • @fallonronin2178
    @fallonronin2178 2 года назад

    thank u so much, am studying for my exams are tomorrow appreciate the teaching

  • @mangehgladysleila350
    @mangehgladysleila350 2 года назад +2

    Great video! Your videos are enough to understand any topic.

  • @diamondpk17
    @diamondpk17 2 года назад

    thanks for all your videos on calc. I literally learn more with them.

  • @GaIIoprehistorico
    @GaIIoprehistorico 5 месяцев назад

    Best teacher of the worls

  • @msfreya777
    @msfreya777 7 месяцев назад

    My differentiation skills after watching this video >>>> I can literally do mental calculations now.

  • @nadiameguid7378
    @nadiameguid7378 3 года назад

    You are the best, thanks for all your efforts to make a great videos. You are my favorite during my journey at College.

  • @yfseth4315
    @yfseth4315 8 лет назад +39

    @51:40 you forgot a negative f'(1) is -3 not 3

  • @aesthete8237
    @aesthete8237 4 года назад +18

    37:00- you forgot the squared-exponent of tan(5x+8)
    It should be... 30x[tan(5x+8)]^2[sec(5x+8)]^2
    But great video though☺

    • @butyrate
      @butyrate 3 года назад

      Yeah I noticed that too...

  • @TheLokomente
    @TheLokomente 2 года назад

    STEM’s MVP channel

  • @jgoemat
    @jgoemat Год назад

    Something that helped me see it wasn't just a black box where you have to follow rules without understanding them was trying it with just a power of x. The derivative of x^8 is 8x^7. What if you use the product rule to find the derivative of x^5 * x^3? f'(x) is 5x^4, g'(x) is 3x^2. So you get (5x^4 * x^3) + (x^5 * 3x^2). That's 5x^7 + 3x^7, or 8x^7, the same as if you combined them.

    • @amerali4406
      @amerali4406 Год назад

      How you doing buddy, sorry n0 buddy responded to you

  • @johnkiiru7429
    @johnkiiru7429 3 года назад +23

    review your video at time"37.08", a power 2 went missing at some point

  • @maryva867
    @maryva867 Год назад

    In the final answer for the composite chain rule, it should be tan^2(5x^2+8)

  • @msfreya777
    @msfreya777 7 месяцев назад

    You're always so gooood, but this time I think at 37:07:- you forgot to put the square above the tan(5x^2+8) in the last line.

  • @hermelagetaneh4386
    @hermelagetaneh4386 5 лет назад +2

    U make my life easy thank u for helping me really

  • @Hellylali
    @Hellylali 2 года назад

    You're my savior hehe but u forgot about the negative sign on 3 (table part) It's actually supposed to be 44/4 and so the answer is 11 not 23/2

  • @fat6776
    @fat6776 2 года назад +3

    Chain Rule happens at 18:00

  • @hirahasan21
    @hirahasan21 3 года назад +5

    This was extremely helpful, thank you!

  • @Amol-w2v
    @Amol-w2v Год назад

    You’re the best
    Alway!!!!

  • @cory4577
    @cory4577 3 года назад +1

    Thank you so much, you make it so easy to understand !

  • @joshr168
    @joshr168 8 лет назад +5

    Great video! Shows a lot of good info.

  • @jpm80
    @jpm80 2 года назад

    i love you organic chemistry tutor

  • @nebulasfun7146
    @nebulasfun7146 2 года назад +1

    You are best bro

  • @omgplays169
    @omgplays169 3 года назад

    Lots of love from Pakistan ❤️❤️❤️

  • @SamAccountLink
    @SamAccountLink Месяц назад

    the desc: It also covers a few examples and practice problems on the product and quotient rule. also the vid: 1 hr of examples

  • @fathiaa493
    @fathiaa493 Год назад +1

    at 51:54 you put 3 instead of negative 3, the answer is 34/4.

  • @ADISUGEMECHU
    @ADISUGEMECHU Год назад

    thank you teacher

  • @harindalal3978
    @harindalal3978 2 года назад

    Very nicely explained.

  • @MohamedAhmed-op6zh
    @MohamedAhmed-op6zh 3 года назад +1

    You made an error. 52:29 it was supposed to be 36/4 which then h(1)=9

  • @robintuition4164
    @robintuition4164 5 лет назад +24

    Hi! Not sure if you will see this, but thought I would try. Thank you for these videos, they are helping me a lot. Question though: @ 37:09 you give the final answer but don't include the ^2 on [tan(5x^2+8)]. Shouldn't it be 30x[tan(5x^2+8)]^2? Is there a rule that I am missing where that shouldn't be included? Thanks!!

    • @rafiatbm7867
      @rafiatbm7867 5 лет назад +2

      Yeah thats a wrong answer....

    • @rafiatbm7867
      @rafiatbm7867 5 лет назад +7

      30x[tan(5x^2+8)]^2[sec(5x^2+8)]^2 is what I got...Plz correct me if I am wrong

    • @wildlifeadventuregirl
      @wildlifeadventuregirl 4 года назад

      @@rafiatbm7867 Yeah that is correct

    • @wilson15car
      @wilson15car 3 года назад +1

      @@rafiatbm7867 Yh that’s correct which can also be written as 30xTan^2(5x+8)Sec^2(5x+8)

  • @nadeshaclayton4918
    @nadeshaclayton4918 2 года назад

    This is very helpful

  • @Clayvalue
    @Clayvalue 7 месяцев назад

    1 thing I notice is that in my calc class, the equations are NEVER this simple. And I can NEVER find any complex product chain rule examples online

  • @kabandajamir9844
    @kabandajamir9844 Год назад

    So nice

  • @giromcannedelima5670
    @giromcannedelima5670 3 года назад

    I was really thinking about that 15:00

  • @zoyakaira4422
    @zoyakaira4422 2 года назад

    Thank you so much 😊

  • @georgephillip6049
    @georgephillip6049 6 лет назад +2

    Thanks a bunch!👍👍

  • @blacktrout
    @blacktrout 3 года назад +1

    When your midterm is 10 questions in 75mins so you have 7.5mins to do problems that take you 30 mins each to do.

  • @jonathanpacheco9680
    @jonathanpacheco9680 7 лет назад +7

    gracias :) podrias hacer analisis de funciones por favor

  • @aquariusgal
    @aquariusgal 3 года назад

    you're my king

  • @jensstefan2475
    @jensstefan2475 Год назад +1

    At 21:15, how is this derived? That is, why dy/dx = dy/du * du/dx?
    I understand the logic that follows but why does he reach this conclusion in the first place?

  • @mirom7167
    @mirom7167 2 года назад

    at 51:52 u forgot to carry the negative . it should be -3 wich makes h'(x) 36/4 wich is 9

  • @ishimwehonore8042
    @ishimwehonore8042 2 года назад +1

    How to form a differential equation from y=AX^2+B/x+C/X^2 where A,B,C are orbitary constant?

  • @AbidxArman
    @AbidxArman 3 года назад +1

    Watching in Master Economics 🙄!!

  • @maki3858
    @maki3858 4 года назад +2

    ahhhhh thank you so muchhhhh

  • @issatay8876
    @issatay8876 2 года назад

    good video

  • @emmanuellefevre8729
    @emmanuellefevre8729 2 месяца назад

    If you’re asked to find the y value for the equation of the tangent line how would you do it if you have the slope already and they give you the x value

  • @johndionellelistana5072
    @johndionellelistana5072 Год назад

    Thank you. It was very informative.

    • @sanopann1896
      @sanopann1896 Год назад

      big bro help me i just want to know becuase I'm confused at 35:05 why there is a 2x next to the cos when the outside is just sin

  • @arianitmustafa
    @arianitmustafa 2 года назад

    DX - D GENERATION X

  • @Jamesb570
    @Jamesb570 2 года назад

    thank you very much

  • @roa1437
    @roa1437 3 года назад

    THANK YOU

  • @ferry6700
    @ferry6700 4 года назад

    Great thanks 👍

  • @antsinspring6087
    @antsinspring6087 Год назад +1

    Any econ students

  • @joshuatamer1933
    @joshuatamer1933 5 лет назад +1

    Could you make a video on first principles?

  • @davisb.w2779
    @davisb.w2779 3 года назад

    Excuse 37:09 power of 2
    But thanks anyway learnt

  • @alfredchirwa6878
    @alfredchirwa6878 2 года назад

    The tan function should be squared tan^2 in the final answer

  • @kamilamohamed284
    @kamilamohamed284 2 года назад +1

    Watching 00:15Am

  • @jordandelosreyes5656
    @jordandelosreyes5656 2 года назад

    43:38 - Personal Bookmark

  • @siyonanaidu4693
    @siyonanaidu4693 2 года назад

    at 36:37 the answer is missing a ^2 on the tangent

    • @sanopann1896
      @sanopann1896 Год назад

      big sis help me i just want to know becuase I'm confused at 35:05 why there is a 2x next to the cos when the outside is just sin

  • @AHMEDALFourjani1998
    @AHMEDALFourjani1998 6 лет назад

    Thanks 👍

  • @omachi1040
    @omachi1040 2 года назад

    At 57:17 why didn’t you multiply 6 with 0. Isn’t the equation like g’(f(x)) • f’(x)? So shouldn’t we multiply 6 with 0 because it’s the f(x) inside the g. And then multiply it with f’(x) so the answer would be 0 and not 42

  • @harshsanatani1699
    @harshsanatani1699 4 месяца назад

    I have a doubt, at 39:46, shouldn't the Tutor say, "The example is a combination of product rule and chain rule" instead of "The example is a combination of product rule and quotient rule". Am I missing something here?

  • @andrewmwale6238
    @andrewmwale6238 Год назад

    cheers chears.

  • @saadfadel924
    @saadfadel924 Год назад

    58:46 is 2(-3) not 2(3)
    f' of 1 is equal to -3