Product rule | Taking derivatives | Differential Calculus | Khan Academy

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Khan Academy

Khan Academy

Күн бұрын

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@1995Rebel
@1995Rebel 10 жыл бұрын
Honestly your making me want to cry. The fact that i can understand a concept so thoroughly from a youtube video, opposed to my professor, is worrying. Thanks a lot whoever is behind this
@13rwi
@13rwi 10 жыл бұрын
the man the myth the legend..... Sal Khan
@monkeyman9276
@monkeyman9276 6 жыл бұрын
none unknown bruh that was posted 3 years ago
@aricroy4258
@aricroy4258 6 жыл бұрын
maybe you're not paying as much attention in class then you are in a KZbin video.
@gamescape2798
@gamescape2798 5 жыл бұрын
you're*****
@Euthenon
@Euthenon 2 жыл бұрын
Lmao, this comment really was posted when I was 10 years old and in 4th grade, now I’m a few weeks away from graduating high school. And this video... it was posted when I was just three years old.
@bluesnote1
@bluesnote1 7 жыл бұрын
It's sad that a video from exactly 10 years ago from today (10-3-2017) taught me more in 10 minutes than a 2.5 hour lecture by someone who gets paid to teach it.
@closetedmilenialschizopers8734
@closetedmilenialschizopers8734 7 жыл бұрын
They're doing their best. Cut them some slack. It's not fair to compare your teachers (mere mortals) to the almighty maths GoD that we know as Sal.
@garr6448
@garr6448 5 жыл бұрын
Closeted Milenial Schizo person dude “mere mortals” 😂😂😂
@shazma803
@shazma803 5 жыл бұрын
@@closetedmilenialschizopers8734 yaa hail sal lol
@sanugabimsara1289
@sanugabimsara1289 5 жыл бұрын
from year 2020 here
@adityabp7973
@adityabp7973 4 жыл бұрын
@@sanugabimsara1289 same here
@t0x1cear34
@t0x1cear34 7 жыл бұрын
I'm glad I found this channel... Tomorrow is my maths exam re-test... (Bcz i failed in the first one) and I didn't understand this chapter... Now I've understood it properly
@notchloe
@notchloe 15 жыл бұрын
I have gone back to school (quite a mature student) and am starting my degree next semester, you have made me feel so confident i can do it. Many thanks good sir :D
@SergioBuilds2000
@SergioBuilds2000 3 ай бұрын
how did you do?
@TheFishWhat
@TheFishWhat 13 жыл бұрын
I'm in AP Calc and you, sir, have saved my life, and possibly the lives of everyone I know. Hats off to you.
@DarrellVermilion
@DarrellVermilion 15 жыл бұрын
It must feel good to see all these positive comments, and you deserve each one. The teaching methodology you employ in your videos is extremely learner-friendly, and lends itself to people who aren't intuitive when it comes to mathematics. Kudos.
@donkamzy6607
@donkamzy6607 3 жыл бұрын
13years later you're still saving lives
@adharsh69420
@adharsh69420 3 жыл бұрын
Yup
@RunningToday77
@RunningToday77 6 жыл бұрын
I don't know who you are, but you sir, are my hero. I hope you're getting the recognition you deserve for the help you provide students on the daily.
@82cricri
@82cricri 7 жыл бұрын
My professors should be sending you a percentage of their paycheck!
@sirjain4408
@sirjain4408 4 жыл бұрын
HA
@hamdaaqilalvi
@hamdaaqilalvi 3 жыл бұрын
This has helped me so much. I have my exam tomorrow and I couldn't understand so many topics because I was basically moping around and my teacher is pathetic but I came her today and BOOM! Thank you so much Khan! Whoever is behind this! ❤️ I want to give a hug to you.
@parkourbigbird2378
@parkourbigbird2378 7 жыл бұрын
Give this man a Nobel Prize
@david0aloha
@david0aloha 14 жыл бұрын
Oh, and for anyone else who reads this, it really helps to go along with a pencil and paper (I use a lap sized whiteboard and dry-erase markers) and solve it as Sal does. I like doing it in lectures, but it works even better with the videos since you can pause it if you need more time (and I find actually doing it to be one of the best ways to remember how to do it later, plus you can absorb Sal's intuition while doing that).
@kaibowes
@kaibowes 7 жыл бұрын
Funny, my midterm is tomorrow and I'm watching/learning this exactly 10 years after it was uploaded. October 3, 2007 - October 3, 2017.
@TheQB1999
@TheQB1999 6 жыл бұрын
And here I am in the same boat, another year later xD
@z-man1938
@z-man1938 6 жыл бұрын
And after a month here......
@adriancres8598
@adriancres8598 5 жыл бұрын
After a year ;)
@aliwa5175
@aliwa5175 3 жыл бұрын
@@adriancres8598 after a year (:
@krishagarwal1844
@krishagarwal1844 3 жыл бұрын
my midterm is tomorrow!
@vibhavpandey280
@vibhavpandey280 7 жыл бұрын
Give this man A Noble prize already. GOAT!
@novaastronomia8720
@novaastronomia8720 3 жыл бұрын
How which category? For what research?
@matiassantacruz5487
@matiassantacruz5487 6 жыл бұрын
I really don't understand how the hell it's possibly for you to be so understandable, it's almost as if your brain is connected to mine and just feeding the information into digestible chunks. Thanks so much!!!
@notoriouswhitemoth
@notoriouswhitemoth 9 жыл бұрын
I hope no one minds my pointing out, here's a much simpler way to illustrate the product rule, that also reinforces a more basic derivative: f(x)=x*x f'(x)=(x*1)+(1*x) f'(x)=x+x f'(x)=2x
@sirjain4408
@sirjain4408 4 жыл бұрын
You ARE right, but that is a short cut. he is showing the actual definition for beginners
@PenandPaperScience
@PenandPaperScience 3 жыл бұрын
I do exactly similar exercises, showing the product rule works on examples where we already know the answer :) It's a great way to see that it actually works!
@novaastronomia8720
@novaastronomia8720 3 жыл бұрын
You are correct in the basics but you missed that the product rule is the simple solution.
@NicholasVLee
@NicholasVLee 8 жыл бұрын
Sal, you're the only one who's doing all the tutorials for all the subjects?
@rarukuxcarung3706
@rarukuxcarung3706 6 жыл бұрын
He mainly does the math subject, but he also does some of history, but not all of it. It's a diffrent teacher that does it.
@azlanmulani6983
@azlanmulani6983 Жыл бұрын
This video is as old as me yet more informative than my teachers
@raphreyn
@raphreyn 15 жыл бұрын
I learn WAY more from you than I do from my college classes. Thanks
@Sl1f3rDrag0n
@Sl1f3rDrag0n 8 жыл бұрын
I've learnt more about the chain and product rule in the past 9 minutes than I did in a whole semester
@McStebb
@McStebb 13 жыл бұрын
I'm pausing the video every time you write an example problem to work it out before you do. It helps a whole hell of a lot.
@DirtyTriks
@DirtyTriks 13 жыл бұрын
Thanks for the explanation. I'm very happy that there are people out there in the world that can help the struggle.
@Casadeldank
@Casadeldank 12 жыл бұрын
youre amazing, Even though i have a really good calc teacher, i can always supplement the lectures with your videos and it really is making things easier. Thanks you so much
@maxmaxmaxfelixfelixfelixlo1052
@maxmaxmaxfelixfelixfelixlo1052 Жыл бұрын
Jesus Christ I never understood a thing in my calc course and this will certainly help my calc quiz tmr! Thanks alot! From 2023 btw
@seanyoman
@seanyoman 12 жыл бұрын
thank you sooooo much. we were "shown" how to do this in class today. my teacher barely explained a thing. this, and your other videos, have helped me so much. again my full THANKS!
@mhengclinkx3468
@mhengclinkx3468 6 жыл бұрын
Me watching this in dec 2018. Thanks a lot to the person behind this, i just don't understand what our teacher teached us but this, its kinda makes me thinks that i actually good at this hahahaha
@MikCish
@MikCish 11 жыл бұрын
omg thank you, i always thought he did it too fast and it all went over my head!!
@leowartsila
@leowartsila 15 жыл бұрын
Hello! I'm from Brazil and I'm really glad I've found your video. I could learn in a few hours what was so hard to get from the books. Thanks a lot!!!
@khanacademy
@khanacademy 17 жыл бұрын
yeah that's right (and the same thing as what is in the video)
@sfaaa7A
@sfaaa7A 10 жыл бұрын
Khan what can i say ! i thought i am really bad and i'll never understand this things . but with you it looks very simple and easy ! Thanks a lot . sorry for my bad English tho
@pecunious07scape
@pecunious07scape 11 жыл бұрын
I've seen a lot of people, or teachers, let their ego get in the way when teaching something especially math. They like to make it as complicated as possible so that you will find it more difficult to understand so that they will look smarter. Khan however doesn't do that. He tries to simplify everything so that it is more understandable, which actually makes him look much starter than those aforementioned.
@SuperChristianMiiworld
@SuperChristianMiiworld 15 жыл бұрын
From now on, you're my new professor... unlike the other one who's a mean grader. Thanks for the vids!
@DarknessHowls
@DarknessHowls 15 жыл бұрын
Awesome! I'm teaching myself calculus with your videos--thanks so much for providing these concise and clear lessons. :-)
@Savware
@Savware 16 жыл бұрын
Dr. Khan is what I'm gonna call you coz u bring pride and satisfaction to the teaching of the mathematical discipline...PS You are the Bomb + U have a sizable population of FANS in India!
@TheGreatBrendon
@TheGreatBrendon 13 жыл бұрын
You have pretty much carried me through Math, Biology and Chemistry through year 11 and 12 :P
@alopeciachimp
@alopeciachimp 5 жыл бұрын
I love you You saved my life😍😍😍😍
@EdwardCullensMayo
@EdwardCullensMayo 13 жыл бұрын
sal you're the man. product = quotient rule saves me much confusion. i'm teaching myself calculus before i take it in the fall and i'm beasting this material so far. thanks so much.
@zeeiggy
@zeeiggy 16 жыл бұрын
excellent 5 stars excellent :), you're so great at teaching that I actually tell my friends that you're my tutor.
@sarev.
@sarev. 8 жыл бұрын
I totally understand how to do it now! only thing I don't get is how do you simplify it? (currently doing a summer project for calculus & I can't remember much) 😩😭
@dawoodgoga6616
@dawoodgoga6616 10 жыл бұрын
I finally learned this stuff properly, thanks so much, i hope you upload more complex examples of chain and product rule as well the Quotient Rule
@samshreds16
@samshreds16 7 жыл бұрын
Dawood Goga I
@koyal99
@koyal99 14 жыл бұрын
omG I struggled so much with this in class today but after watching your videos, it is sooooooo easy!
@ShenoyKitchen
@ShenoyKitchen 7 жыл бұрын
hey man u deserve a nobel 👍👌👌👏👏
@tomdanvlog
@tomdanvlog 13 жыл бұрын
@DryBones111 Multiply two variables together. When they're adding, you can just derive them separately and add them together after, but when they are multiplied, you have to use this rule.
@danottob
@danottob 12 жыл бұрын
Im in college right now and i just don't go to the class, other than to take the tests so you've got a great idea
@nohackers2037
@nohackers2037 5 жыл бұрын
u(dv/dx) + v(du/dx) very similar to quotient rule (v(du/dx)-u(dv/dx))/v^2
@brookitha327
@brookitha327 6 жыл бұрын
I like how you change the color to be more pleasant :)
@drewsteps
@drewsteps 12 жыл бұрын
I'm in college, and I'm already doing this. It works!
@14cvanrensburg
@14cvanrensburg 13 жыл бұрын
You sir just saved my grade in honors calculus, i am forever in your debt
@cookieeatbird
@cookieeatbird 15 жыл бұрын
you got it. Well it's arbitrary now, but when you get more into it you'll see that the dy/dx makes a lot of sense.
@flamurbedrolli802
@flamurbedrolli802 4 жыл бұрын
for example 2^2 * 2^2 = 16 . you can write it also as 2^2 *2 + 2^2*2 = 2(2^2+2) = 2 *(2^3) = 2^4 = 2^2 * 2^2 = 16 . The product rule .
@stelladavis1798
@stelladavis1798 5 жыл бұрын
We just started derivatives and I had already known the power rule, and the addition and subtraction rules too. I was using the difference quotient on the problems to practice because they were easy problems and just using the other rules to check. I was planning on breaking those out on the test to save time, but then one kid in my class said he found a shortcut (he figured out the power rule) so my teacher said he was taking all of the polynomials off the test. So now I'm learning the other rules so I can ace the test in ten minutes I mean he can't say I'm cheating if I prove the math
@LGseeker
@LGseeker 9 жыл бұрын
This is fun👍🏼 thank you
@runningfromManda
@runningfromManda 13 жыл бұрын
I'm a student at CU Boulder and I think you just saved my calculus grade.
@Liquid780
@Liquid780 16 жыл бұрын
YOU are a friend to the WORLD!
@bandianitha1811
@bandianitha1811 8 жыл бұрын
awesome I have improved a lot just because of ur videos thank u!!!
@muslimahtutoress266
@muslimahtutoress266 2 жыл бұрын
Great video, I like that you used high positive and negative powers for variables. I believe it exposes students to problems that they would not be too frightened of, especially when a test/exam comes up.
@8bit_pineapple
@8bit_pineapple 16 жыл бұрын
It's really simple take for instance 2^4 that's 2 time 2 times 2 times 2 so 2,4,8,16 ... 16 if you divide 16 by 2 (8) it should equal 2^3 that's 2 cubed or 2 time 2 times 2... so 2,4,8 which it does!!! so all you do to reduce a power by 1 is divide by the coefficient (that's the number in front of the power) ... using that we can find out 2^4=16 divided by 2 2^3=8 divided by 2 2^2 =4 divided by 2 2^1=2 divided by 2 2^0= following the pattern you see 2^0 = 1 as 2/2 = 1
@zoroluva
@zoroluva 15 жыл бұрын
I got killed in calc 1 because my teacher could not break this stuff down like Khan does. Thanks man. I wish I knew about this channel earlier.
@david0aloha
@david0aloha 14 жыл бұрын
I do it in the reverse order of you - I find it simpler. I posted it in the last video. I go from out function to inner function. Thinking about it like a tree, it allows me to go from the single branch to the other branches one-by-one. I find that makes complicated instances of the chain rule much easier since the structure naturally sorts itself out without my figuring out what term goes where (I posted an example in the last video). Thanks for the videos Sal, this is still good review!
@Ilovemusicful
@Ilovemusicful 4 ай бұрын
Excellent explanation of Chain Rule but I would like to see the last bit of simplifying the answer too...Thanks
@muddy218
@muddy218 15 жыл бұрын
Why didn't I find these videos months ago? They help so much!
@jonathanibarra8236
@jonathanibarra8236 6 жыл бұрын
Khan your great and thank you cuz I finally understand calc but plz continue to talk slow cuz your new videos you talk to fast and its harder to grasp
@discuss2130
@discuss2130 10 жыл бұрын
Making up ad hoc examples produces unique results. Guess is no easy way to make this more interesting for people.
@derekmurphy201
@derekmurphy201 11 жыл бұрын
This guy is a freaking genius! I wonder if he does private tutoring
@Enigma415
@Enigma415 15 жыл бұрын
THANK YOU! dy/dx always confused me, although I knew there was something like that I couldn't be sure... now I know: f'(x) = dy/dx = (something arbitrary)!
@Ayush1206
@Ayush1206 9 жыл бұрын
Sal ur the real MVP !!! ur videoes help me understand theses concepts in such a good manner.....thank you
@scootcity4
@scootcity4 8 жыл бұрын
at 7.17, should it not go from -5 to -6 instead of -4?
@chriseldridge5655
@chriseldridge5655 5 жыл бұрын
I made that exact mistake too, thanks for posting it so I could see Unli Revs's response
@chriseldridge5655
@chriseldridge5655 5 жыл бұрын
@Unli Revs Thanks for posting this clarification
@ameluk7064
@ameluk7064 11 жыл бұрын
thank you for your fully explain to me! i didn't pass before, when i watch your videos i got pass !!! thanks so much :D
@Andrea_Betty
@Andrea_Betty 12 жыл бұрын
You sir, are a life saver.
@monicaroberson9030
@monicaroberson9030 7 жыл бұрын
no like i love you..like honestly
@turmoil9
@turmoil9 11 жыл бұрын
these videos are so good that they don't even need to be above 240p
@vikassaini1935
@vikassaini1935 5 жыл бұрын
first i watched this video when i was in high school and now i am watching this in my computer science degree for revision to do artificial intelligence
@AM-nl5yo
@AM-nl5yo 6 жыл бұрын
Wooow ' you have 3 million follows i ma really happy for you 👏👏👏👏🌷 Thank you i can understand now 🤜🤛
@8bit_pineapple
@8bit_pineapple 16 жыл бұрын
Think7 as 7x^0 (any thing to the power of zero is one) times the number in front of x by the power (7 times 0) equals 0 take one off the power and you get 0x^-1 which is 0 divided by x which is zero (or you can just think anything times 0 is 0 so 0 times x^-1 must be 0) The reson anything to the power of zero is one is because you have to divided the number by itself to get to zero... e.g. 2^3 (8) divided by 2 is 2^2 (4) divided by 2 is 2^1 ( two) divided by 2 is 2^0 (or 2 divided by 2 is 1)
@Altare1994
@Altare1994 12 жыл бұрын
Just watch his playlists on whatever course you plan on taking, test on it (Clept) and opt out of it. Save money, graduate faster, learn more.
@ChristewieTV
@ChristewieTV 14 жыл бұрын
Here I am fretting and hyperventilating and after watching you explain it everything clicked. Thank you
@TheGhid
@TheGhid 14 жыл бұрын
this guy make it so simple
@johnhwen1
@johnhwen1 15 жыл бұрын
Wow! These lessons make so much sense! Thank you so much!
@winxie97
@winxie97 5 жыл бұрын
thank you for this, I get lost with the problems similar to the last one
@BabyEnginee0
@BabyEnginee0 6 ай бұрын
It's like traveling on time🎉🎉🎉
@modeyrawa7iz595
@modeyrawa7iz595 5 жыл бұрын
Thank you so much, you are the best sir
@xiahaha
@xiahaha 13 жыл бұрын
1. Use the definition of the derivative to calculate the derivative f′(x) of f(x) := x + c, where c is a constant. Using this, and the product rule, differentiate the function g given by g(x) := (x + 1)(x + 2). Check your answer by expanding the formula for g(x) and then differentiating. How would you do this? lol
@GTSD00D
@GTSD00D 15 жыл бұрын
thank you!!!! im gladly donating
@apolllos7
@apolllos7 12 жыл бұрын
Thanks : ) endless Calculus homework for me
@PenandPaperScience
@PenandPaperScience 3 жыл бұрын
For those that want some more practice, I just uploaded a video where I solve such exercises step-by-step, perhaps that might help :)
@AnuragSingh-iv7zv
@AnuragSingh-iv7zv 7 жыл бұрын
thanks sir for making me understand the chain rule
@DiamondMind
@DiamondMind 14 жыл бұрын
Es la calma de la arena Golpeada por el mar Esa calma que hay en todos Frágil como un cristal Que nos dice y que nos cuenta Que el amor traerá... calma
@GreyAlien502
@GreyAlien502 12 жыл бұрын
its the quotient rule video. you can find all the videos in the calculus playlist :)
@DirtyTriks
@DirtyTriks 13 жыл бұрын
@ChemaShima No, he has it correctly. The original in equation is 3x^ -3 and not 3x^ -5.
@Sorrownighty
@Sorrownighty 8 жыл бұрын
last 1 blow my mind
@Freeze00201
@Freeze00201 12 жыл бұрын
@TheFashionvictim6 I believe the answer is 48. dy/dx = 3(-2x)^2. Then you said x = 2, so...substitute -- 3(-2(2))^2 = 48.
@helllodarling
@helllodarling 11 жыл бұрын
I never took calculus in high school, but am taking it in first year uni. I'd probably fail if it weren't for you!
@saroolicious1
@saroolicious1 16 жыл бұрын
pure genius =D
@Sp0okeh
@Sp0okeh 11 жыл бұрын
wait what wth, 7:16 is that "(3x^-5" or "(3x^-3"? you did say "-3" but i read "-5"...
@larmar52
@larmar52 11 жыл бұрын
i think he messed up its supposed to be -15x not -9x
@kevinpatel8186
@kevinpatel8186 10 жыл бұрын
123IGRACH actually Sal did it right because the orginal problem is 3x^-3
@rubenleyva3006
@rubenleyva3006 11 жыл бұрын
I wish I would of found these videos before failing my calculus class
@mohammadpourheydarian5877
@mohammadpourheydarian5877 4 жыл бұрын
Typo: f prime in 2:20 and not =
@shapeurmind
@shapeurmind 14 жыл бұрын
I love it when he says: "This will optimally confuse you" xD...
@eazycheez1432
@eazycheez1432 6 жыл бұрын
THANK YOU MAN!! A LOT
@MrJuandahero
@MrJuandahero 6 жыл бұрын
4:07 Why did we get rid of the " -7 " ?
@sanveersookdawe
@sanveersookdawe 6 жыл бұрын
Because it's a constant
@LAnonHubbard
@LAnonHubbard 14 жыл бұрын
Awesome, thanks!
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