Chain Rule Examples

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  • Опубліковано 9 лют 2025
  • Examples using the Chain Rule
    Practice this yourself on Khan Academy right now: www.khanacadem...

КОМЕНТАРІ • 349

  • @ftit5893
    @ftit5893 5 років тому +167

    Normal teachers: explains the simple questions and leave us with the hardest
    Khan: explains the hardest and makes us feel that calculus is fun

    • @r4fa3l59
      @r4fa3l59 4 роки тому +2

      But calculus is fun, indeed :/

    • @aaaaaa-rr8xm
      @aaaaaa-rr8xm 2 роки тому

      @@r4fa3l59 these q isnt even that hard

    • @sagnikbiswas3619
      @sagnikbiswas3619 2 роки тому

      Facts

    • @Javiertennis2044
      @Javiertennis2044 4 місяці тому

      My teacher said we'll have to do 12 functions inside of 1, though. Lots harder.

  • @BB-co9jn
    @BB-co9jn 8 років тому +95

    This site has improved my grades immensely for several challenging college courses. Thank you.

    • @sterlingarcher3981
      @sterlingarcher3981 7 років тому

      B E I take calculus and vectors in high school

    • @dytn959
      @dytn959 7 років тому +18

      Sterling Archer cool no one cares

    • @JamesTownsendJian
      @JamesTownsendJian 6 років тому +7

      @@sterlingarcher3981 r/IAmVerySmart

    • @selfrighteousduck9151
      @selfrighteousduck9151 3 роки тому

      @@JamesTownsendJian bet, I am an 11 y/o who learned this for fun without problem, redditor

  • @GreaterDeity
    @GreaterDeity 11 років тому +14

    Seriously, I would fail calculus if it were not for these videos. I cannot tell you how large of a service you are doing the student community by posting these. You have my deepest gratitude. I'd be happy to donate resources for your services here!

  • @TheAlmightyNivs
    @TheAlmightyNivs 10 років тому +98

    My prof is great but hearing someone else explain it is just that much more helpful.

  • @singularityeh6002
    @singularityeh6002 8 років тому +38

    I swear I will donate as soon as I can as you deserve it khan academy.

  • @smartconjurers2509
    @smartconjurers2509 4 роки тому +38

    The highest quality content available in the lowest quality
    graphics!!

  • @apexpredator9021
    @apexpredator9021 7 років тому +33

    In this example you have applied the chain rule once. In some tests it requires you to apply the chain rule until the inner function is at its simplest, so very basically you are left with one x and a number. That is why its called the chain rule: because you can continuously apply it until you reach 0.

    • @sanchitabardhan7301
      @sanchitabardhan7301 7 років тому +1

      So basically is the derivative = derivative of the inner function * exponent! ?

    • @kimmarch90
      @kimmarch90 3 роки тому +1

      I have been noticing this too. My professor takes steps so much further and expects us to do so also. :/

    • @No_BS_policy
      @No_BS_policy 2 роки тому +1

      First order derivative. Only higher order derivatives require iteration of the chain rule.

    • @oldprofile17
      @oldprofile17 2 роки тому +2

      @@kimmarch90 It's been a year but if it still confuses you, it makes more sense when you think of the exponent*thederivative has some constant (A) and apply the
      d/dx Af(x)=Ad/dx f(x)=A*f'(x)
      rule. Then repeat the chain rule.

  • @eron6362
    @eron6362 9 років тому +250

    Back in the days of 240p...

    • @rayhanmansoor2951
      @rayhanmansoor2951 5 років тому +10

      Back in the days of 1080p....

    • @dhruvupreti5120
      @dhruvupreti5120 4 роки тому

      @@rayhanmansoor2951 though they have now come back!

    • @zeyadalabdaly3393
      @zeyadalabdaly3393 2 роки тому +1

      To be honest it looks much more fun, entertaining, and captivating.

  • @1010nedim
    @1010nedim 12 років тому +2

    im spending a fortune at university and learning 1/5th of the information i learned in this video
    big ups :) and a BIG thank you!

  • @Bloodsaberxy
    @Bloodsaberxy 16 років тому +2

    i have never had a teacher this great... bless you man, you're just amazing at what you do

  • @vashistaditya4150
    @vashistaditya4150 6 років тому +6

    Mr. Khan, you are a beast! The way you explain is amazing.

  • @kream013
    @kream013 14 років тому

    i agree with all these people who find this video soooooooooo helpful....i was trying to study this in my calc1A text book and the longer i tried to understand the chain rule the more confused i got. this video makes it so clear. thanks a lot.

  • @bartoszprzybysz5416
    @bartoszprzybysz5416 Рік тому

    I've been out of school for about 5 years now. Thinking about going back tor a mathematics degree I never finished as a Computer Science major. I have to say, Khan is more coherent than most of my university professors I've ever seen!!

  • @TheEliteBalla
    @TheEliteBalla 11 років тому +2

    You sir, are a hero above all heroes.

  • @pro4skill
    @pro4skill 14 років тому +1

    amazing... I watched these videos non-stop, and now I'm going to be ahead in calculus! (I'm in precalc)
    Thanks so much!

  • @lotslepy
    @lotslepy 14 років тому

    the world needs more people like you, sal.

  • @steelguts777
    @steelguts777 13 років тому +3

    These videos are amazing, I love how you are direct and straight to the point wasting no time at all. I am definitely recommending you to all of my friends :-)

  • @bayekofsiwa5847
    @bayekofsiwa5847 9 років тому +5

    Thank you always, Khan Academy! You are the best!

  • @indirasrinivasan9711
    @indirasrinivasan9711 8 років тому +4

    +Khan Academy I just wanna say you are doing a marvellous job explaining the content of all your videos. You are the reason I could intricately understand certain concepts. Thanks a lot!! xoxo

  • @JNorth87
    @JNorth87 16 років тому +2

    1925 views by today, in one year, this will have 1 million +
    Thanks, Sal!!!!

  • @ChrisGilbert1
    @ChrisGilbert1 14 років тому +1

    I have spent days trying to learn this and you taught it to me in 10 min. Awesome videos. Thanks for the help.

  • @Aukatrau
    @Aukatrau 14 років тому +2

    I'd give you 5 stars but I can only give you a thumb up. Thanks for explaining stuff in such a clear manner. You are going to be the sole reason I pass AP Calculus.

  • @saminm1
    @saminm1 13 років тому

    I'm 16 and i understood this rule.
    Thank you so much.
    I watch your videos because they are entertaining.

  • @shadowking255
    @shadowking255 4 роки тому

    you are just changing the world man.That is something you should be proud of

  • @xzxz619
    @xzxz619 16 років тому +1

    A kid with rudimentary math skills can learn this!!!
    Are you a some sort of math GOD?

  • @vibha9590
    @vibha9590 3 роки тому +1

    FOR THE MILLIONTH TIME, THANK YOU !!!!!!!! .

  • @LittleMissSpunky
    @LittleMissSpunky 11 років тому

    You didn't confuse me, very clear!! thank you. I am a maths tutor and I usual only tutor year 10 and bellow but I was recently given a year 12 student who "cries when it comes to methods, the whole class does" (His words!) this will greatly help me get him to understand this!!! so thank you again!! :D

  • @VBSyd
    @VBSyd 9 років тому +27

    The derivative of f(x) in the first example looks more complicated than f(x) to be honest...

  • @DanielSmashGaming
    @DanielSmashGaming 12 років тому

    I tried watching a different set of lectures first and they made next to no sense, but everything you say makes absolute sense! Thank you!

  • @CautiousCrow
    @CautiousCrow 14 років тому

    I got a 102% in pre-cal with your help, now its summer time and learning calculus too! Wish me luck on AP Calculus the coming year hehe :)

  • @party360Li
    @party360Li 13 років тому

    i been struggling in calc this whole time n i tried my best to learn my text book n the more i tried the more it confused me but after watching your videos for d first time itself it all made sense...THANK YOU SO MUCH.. I DONT KNOW WHAT I WOULD HAVE DONE IF I DIDNT FIND YOUR VIDEOS. :)

  • @omgim18
    @omgim18 14 років тому

    i love you. u are so much better than my math prof who just doesnt even make sense. i think u are going to be the only reason y i pass my midterm tomro. THANKS. u are doing an amazing job. keep it up!

  • @rasmushougaard646
    @rasmushougaard646 Рік тому

    These calculus videoes are top notch, better than education at universities and paid courses

  • @Primitive_Code
    @Primitive_Code 6 років тому +7

    Good video but you should add natural logs, logs, trig fcns as well, that's where the chain rule raps a chain around your head.

  • @monday2471
    @monday2471 13 років тому

    thank you so much for doing this!
    i can never learn properly in school because my mind wanders a lot, and if i miss even 1 thing the teacher says, i won't understand the entire lesson!
    but i can always replay videos and that's the best part

  • @sabrinakbh
    @sabrinakbh 15 років тому

    A good teacher makes a world of diference.
    Thank you!

  • @nklamusing
    @nklamusing 11 років тому

    Id been having trouble with calculus and its all gone after your tutorials. :) Thanks a ton, Sal!

  • @pakoluevano
    @pakoluevano 15 років тому

    dude you are the best math teacher ever man.... good job i get this stuff man thanks.!!!

  • @shaktikashyap6
    @shaktikashyap6 4 роки тому

    No you didn't confuse us. You r the one of rare best teachers globally. And i really like ur voice and the way you talk. Thanks sir.

  • @Meera781
    @Meera781 12 років тому

    And helping dreams too..I am back to maths after couple of years of break and here I found my class ! God bless you Sir !

  • @millscheeseXD
    @millscheeseXD 11 років тому +5

    still saving lives, i tip my hat off to you sir

    • @theorist353
      @theorist353 3 роки тому

      Hey how's is it going pal
      After 7 years

  • @anitapansari1
    @anitapansari1 11 років тому +1

    Never ever thought I would be smiling after learning Math.... You are math super fun... Loving it and getting confident with every passing video :-)

  • @majingwei
    @majingwei 14 років тому

    Khanacademy saved my life, period.

  • @JoshuaJones-te1ef
    @JoshuaJones-te1ef 5 років тому

    You are a life saver. My lecture is super smart, but you seem to explain it in a more understandable way

  • @dhruvupreti5120
    @dhruvupreti5120 4 роки тому +3

    10mins and a chapter worth of doubts are now cleared!

  • @MuhZubairAli
    @MuhZubairAli 13 років тому

    I have no word to thank you becoz I want give you very very very very big thanks.May God Bless You....

  • @mzdbnell
    @mzdbnell 14 років тому

    This helps me more than my professor. Thankyou sooooo much.

  • @EytanWallace
    @EytanWallace 12 років тому

    U have a completely different face and life than I imagined when I listened to and watched your videos!

  • @topik627
    @topik627 14 років тому

    jazakum'ALLAH'UKHAYRIN! may, GOD bless you and I eveyone else watching these videos!

  • @musk3402
    @musk3402 8 років тому +9

    How is your voice so soothing???

  • @supercoupon2
    @supercoupon2 15 років тому +1

    was waiting on that last set of brackets :) Great job as always.

  • @omfgmedic69
    @omfgmedic69 12 років тому

    Confused me? My teacher confuses me!
    This is what teaching should be, taking time to explain the steps. My teacher taught us the chain rule in one class (2 hours). The next day we were given an in class assignment with the chain rule, but with fractions and rationals. In my head, I was saying ''God help me''.
    Teaching is an art, and thank god there are still some good teachers out there sharing their knowledge for free. Thank you.

  • @bothigati
    @bothigati 8 років тому +15

    i always use your videos to prepare for tests and exams. thanks for making math so much easier

  • @michele7656
    @michele7656 14 років тому

    2:25 "To the minuuus 8." I don't know why, but something about the way you said that was hilarious. Thank you for making these videos and being awesome.

  • @Helllllllnaaaawww
    @Helllllllnaaaawww 13 років тому

    dude u justify the quote that says " I bunk school to study in peace". thanks man . great help

  • @erin210992
    @erin210992 14 років тому

    im studying egineering and i have no idea what i'd do without these vids...

  • @TheRichestCadaver
    @TheRichestCadaver 14 років тому

    Excellent explanation and I learned a lot, so much that I could catch a mistake, somebody also did before me.
    Final answer: [(15x^2-7)(5)(5x^3-7x)^4-6x^-3] (3)[3x^-2+(5x^3-7x)^5]^2

  • @crossfuse
    @crossfuse 15 років тому

    this is soooo much easier for me to understand...i havn't been getting good grades in calc and i think im finally getting caught up

  • @djmauropicotto
    @djmauropicotto 15 років тому

    very good, i want to point out just one thing , in the last problem you need to put a parenthesis "or brackets"in [(15x^2-7)(5)(5x^3-7x)^4-6x^-3] so that way it would be [(15x^2-7)(5)(5x^3-7x)^4-6x^-3] (3)[3x^-2+(5x^3-7x)^5]^2

  • @jrcook-394
    @jrcook-394 5 років тому +1

    This actually makes a lot more sense. My teacher taught us to go outside-in. This is a lot better in my opinion.

  • @TheShelbyiskool
    @TheShelbyiskool 11 років тому +1

    My savior :'). I was scared, and instead of going to church, I went to Khan Academy.

  • @peacefulalien2080
    @peacefulalien2080 9 років тому

    You are explaining 20x better than my teacher . Keep it up good sir ! You're awesome!

  • @goofguy316
    @goofguy316 14 років тому

    YOU ARE A MESSIAH..... Of my marks, thank you so much!

  • @serprex
    @serprex 17 років тому

    Good at explaining with a lack of assumptions, and the mouse writing is clean too

  • @bloodybigballz
    @bloodybigballz 14 років тому

    i actually followed through the whole problem, thank you.

  • @MrSamarthz
    @MrSamarthz 13 років тому

    you didn't confuse us ...you just cleared all our confusions !

  • @0verlordQc
    @0verlordQc 13 років тому

    Thanks for all your videos! Very helpful in exam period!

  • @MissNinita86
    @MissNinita86 10 років тому +52

    I love you.....

  • @XJetBoomX
    @XJetBoomX 11 років тому

    Sal should make a playlist dedicated to teaching "teachers" to teach.

  • @kimshoshi
    @kimshoshi 11 років тому +1

    wow. amazing. thankyou! my $4000 tuition money for the subject would be better off with you...atleast itd pay off by me actually learning something. thankyou soo much

  • @samuelsrinivasvara7681
    @samuelsrinivasvara7681 7 років тому

    So.. so.. so.....good one of the best e-tutors....!!!!!😀😀😊😊😊🌀

  • @anoelst
    @anoelst 11 років тому

    Khan is brilliant!

  • @Alive4Metal
    @Alive4Metal 13 років тому

    Omg... I actually got that.... if my University professor had attempted to teach me this then there is no way in hell i would have followed so clearly.

  • @MarcusGray-b3f
    @MarcusGray-b3f Рік тому

    This review well for me learning for others is great your sessions are well timed so never to long and easy to follow. I forgot how long these calculus problems can get. If I remember correctly some problems can get extremely long.

  • @siriuslyD
    @siriuslyD 15 років тому

    you're so much better than my current calculus professor, THANK YOU!

  • @jhamel
    @jhamel 16 років тому

    this guy is dangerously good.

  • @rifathossain6140
    @rifathossain6140 8 років тому +7

    what a legend

  • @gocanadayayyy
    @gocanadayayyy 11 років тому

    My god I feel so sorry for the people in the comments here that have teachers who don't explain it this way! My math teacher was excellent and she always made sure to go through everything step by step, even when we had two months less than everyone else to do calc (IB is hard). I'm glad these videos are here for people who aren't lucky enough to have teachers this amazing in school.

  • @thebobhannah
    @thebobhannah 11 років тому

    He does that, but in reverse order. Where the brown in the last line is the derivative of the large bracket, the pink times the green accounts for the derivative of the inner portion you mentioned: dy/dx (3x(-2)+(5x(3)-7x)(5). The light blue is the derivative of the last remaining inner portion: dy/dx (5x(3)-7x)(5). I was taught to tackle the outside first, so his method appeared a little backwards to me at first.

  • @the1_1one7
    @the1_1one7 Рік тому +1

    It's about end of 2023 and i hope our dear teacher and all those who commented here are alive and happy 😊
    sorry for my english 😅

  • @Ureyeuh
    @Ureyeuh 7 років тому +1

    I want a shirt with Sal's face smiling inside of a heart.

  • @michelvellve
    @michelvellve 15 років тому +1

    Nice tutorial!
    It really helped me with my homework :D
    Thanks for sharing your knowledge xD

  • @vankhun17
    @vankhun17 10 років тому

    Wow. Your explaination is so short and easy to understand ! thank you

  • @alexandrasvdavis
    @alexandrasvdavis 3 роки тому

    Thanks for all you do Khan Academy

  • @najahdavenport8650
    @najahdavenport8650 5 років тому

    Very Helpful, thankful !

  • @dinamansour3469
    @dinamansour3469 11 років тому

    Thank you so much! Your way of teaching is amazing!

  • @nixenberq
    @nixenberq 15 років тому

    Yeah man, you are awsome, thank you for your lessons !!! Thought I can't learn these things :-D, but its quite clear now, you saved me a lot of time...

  • @manassehleonard2879
    @manassehleonard2879 7 років тому

    You do make maths easier. Thanks Khan.

  • @Chat2Conaz
    @Chat2Conaz 13 років тому

    WOOHOO! Thumbs Up! if your the 100,000 viewer! I love Khan Academy and these videos!

  • @sumankanwar2255
    @sumankanwar2255 4 роки тому

    Best explaination ....👍👍👍👍

  • @paxcoder
    @paxcoder 16 років тому

    You're my online study buddy! Yaay!
    I hope you got many more examples in stock ;-)

  • @Max11551
    @Max11551 17 років тому

    Simply amazing.

  • @MrZia324
    @MrZia324 14 років тому

    great work khan.

  • @cocolombo
    @cocolombo 15 років тому

    Great videos. Thanks.

  • @gideon1103
    @gideon1103 13 років тому

    dude..you are GOOD

  • @PianoSonata
    @PianoSonata 15 років тому

    He's Indian. Such wonderful people. Very educated.

  • @yueting0723
    @yueting0723 10 років тому

    thank you!! my finals on thursday this is very helpful!

    • @BFrei46z
      @BFrei46z 10 років тому

      Mine is this Thursday. How did you do?

    • @Mythrunes
      @Mythrunes 9 років тому

      Bryan Frei Rejected

    • @Mythrunes
      @Mythrunes 9 років тому

      Bryan Frei Rejected

    • @likemyvibe8930
      @likemyvibe8930 9 років тому

      +Mythrunes lol

  • @gdogvibes1
    @gdogvibes1 12 років тому +1

    I know man!!!! I hate that shit, when you get taught something in a simplistic fashion, and they expect you to know what to do when it becomes this complex!!!!!

  • @MsKb1992
    @MsKb1992 15 років тому

    god bless you!
    you make one who hates math turn into a math lover:)
    congrats for finding a faster way in erasing:)
    take care,WE need you.

  • @PoncyPenguin
    @PoncyPenguin 10 років тому +1

    I noticed you wrote a ^2 instead of a ^1, you were showing that there is a ^1 but when you copied it down in yellow you mistook it for a 2 :) Thanks for this anyway