My teacher is so shit when I watch his videos it feels like I'm learning things for the first time. You're the goat thank you
@chciken
3 жыл бұрын
same
@victorquebec5929
10 жыл бұрын
The greatness of this video is in its smooth and logical explanation of the difference between a slope of a secant line and a slope of a tangent! Thank you very much, Sal!!!
@Sameen_The_Business_Coach
2 күн бұрын
R8 It was my 2nd lecture and I'm amazed by the way it was explained.
@mapmemer1897
5 жыл бұрын
God bless this wonderful thing called Khan academy. In 10 minutes I can learn what it took Isaac Newton(I guess) years to figure out.
@shreerangvaidya9264
4 жыл бұрын
Generally the ray of knowledge is a tangent of my brain, thanks for turning it into a secant.
@TheJareWolf
12 жыл бұрын
at 6:26 I hope this clears up any confusion about the 6 + delta x. I was having a tough time with it myself wondering why it wasn't 6 + delta x^2 The reason it is 6 + delta x is because the upper portion should be in parentheses like this: (6dx + dx^2) / dx now what you need to do is factor out dx from the top giving you dx(6+dx) / dx cancel out the delta xs and you are left with 6 + dx If you cant see it, try just using x instead of dx for the sake of clarity (6x+x^2)/x = x(6+x)/x = 6 + x.
@S.Sumedh
2 жыл бұрын
Thank you
@Ruan3843
12 жыл бұрын
Sal you are too awesome, after watching your videos I get the distinct impression that my lecturers are coaching me for exams to boost the pass rate as opposed to making sure that I understand the concepts. Calculus is actually super intuitive, who would have thought!
@TheKvacKaj
9 жыл бұрын
its so funny how this video has half of part 1 views :D
@jamesbentonticer4706
9 жыл бұрын
+Peter Kvačkay I'm sure that results from the 'I suck at math' syndrome.
@ansenliu
3 жыл бұрын
You're so reliable, and in my opinion, books need you too. I have this Pre-Calculus book, and it uses the EXACT same example as you gave, and by the way, it was published 10 years later...so it could've copied you...
@amazin356
11 жыл бұрын
How is 3+dx squared 9+6dx+dx^2, I thought it was 9+dx^2, since you square the 3 and the dx?? Someone help please.
@xxfuggsxx
10 жыл бұрын
you just saved my ass bro
@griftorifto2
13 жыл бұрын
As a testimonial to your awesomeness, i went from an average of 50-75% in math to a whopping 99% in my derivatives test. All thanks to these great vids! 99%! Im still in shock.
@buenobus
11 жыл бұрын
Just as usual, Sal is the master at explaining complex ideas in simple ways.
@ZuccheniMan
11 жыл бұрын
x = delta x... so think of it this way - (3+x)^2 is just (3+x) times (3+x). which is the same as 3(3+x) + x(3+x) which equals 9 + 3x +3x + x^2 - which gives you the 6x
@sterlingarcher3981
6 жыл бұрын
ZuccheniMan thanks man you helped me out
@VFB1210
13 жыл бұрын
For some of those who may get confused with the division of ⌂y/⌂x at 6:27, another way to do the division would be to factor out a ⌂x from the top. The original equation was (6⌂x+(⌂x)²)/⌂x, we can rewrite the numerator as ⌂x(6+⌂x), leaving us with the fraction (⌂x(6+⌂x))/⌂x. We can divide the ⌂x we factored out from 6⌂x+(⌂x)² with the ⌂x on the bottom, which leaves us with the same result: 6+⌂x. Rewriting things with terms factored out is a good way to avoid "hairy math" and careless mistakes.
@Matrik44
14 жыл бұрын
Amazing! everything is so clearly explained. I'm definitely going to be looking at all of your calculus videos! Thank you soooo much!
@mae0o0
11 жыл бұрын
how did it become 6 delta x? I thought you'll just have to multiply it to become 3 delta x. .. ?.?
@JackLloyd
10 жыл бұрын
This is the fundamental derivatives video. I wish he would highlight the videos by cornerstone concepts so that people could know what videos show the end-game of the topics.
@JackLloyd
10 жыл бұрын
123IGRACH That's how I saw it - on Khan. Even on the Website, the organization of the material isn't logically sequential (e.g. parts leading to a whole for mainstream taught concepts.)
@osajukisama777
5 жыл бұрын
Endgame? This comment was way ahead of its time 😮
@dinkylicous1234
14 жыл бұрын
great work, you dont know what a difference you are making to this world. you have pioneered a new form of learning in a much easier and much more understandable way. you sal should be knighted for your time and effort you are giving to the world. you are a generous man who gives up your valueable time to help people whom you dont even know. great work again. from all youtube fans .
@MilanLouboutin
12 жыл бұрын
Where's the 6 delta x from at 4:22 please reply asap, have an exam in two days?
@miguelconfesor4701
4 жыл бұрын
You do the FOIL method
@GabiJunior-ht3xl
5 ай бұрын
An not able to see ur writings
@jakecarlo9950
2 жыл бұрын
@7:45 Why can you “just set [delta x] to zero?” by using the limit? Isn’t this just hand waving as you convert some real distance Delta X - however tiny - to zero for the sake of convenience?
@kamlakumari6227
2 ай бұрын
Ig at last it should be slope of :- f(x)= 6 +∆X so keeping x as 3 answer should be 9 but 6 is written pretty sure it might be a simple mistake but wrote this comment to help anyone else or else understand my mistake
@BruceLeefromthegrave
12 жыл бұрын
@zae4398 he's right, when you divide 6dx +(dx)^2 by dx, the dx divides both 6dx and (dx)^2, 6dx turns into 6 because dx/dx is 1,(some teachers say they cancel each other but not really) 1*6 is 6, while(dx)^2 turns into dx because (dx)^2 is dx*dx/dx which is dx. The numbers are NOT being multiplied. Like if I do 6+9 over 3, the 3 divides both 6 and 9, giving 2+3=6 and if I added first, 6+9=15, 15/3=5, so we get the same result. Know the difference between dividing #'x that are being + and #'s *.
@boubiz3172
Жыл бұрын
dear lord im 19 and have been told that im smart and good at maths multiple times im even studying engineering and here i am trying to understand what a derivative is after calculating more than 202020030303 derivatives for the past 8 years
@renalynramos5509
2 жыл бұрын
Sir... • How to find the slope of the tangent line to each curve when x has the indicated value. • How to find the equation of the tangent line to each curve when x has a given value
@mapa5497
Жыл бұрын
Sir I had one doubt..can we say that the curve had many different slopes..and so we chose a slope and made the equation of that slope as our tangent's equation..
@johndisco5280
9 жыл бұрын
Oh, neow I understand
@uselesssanity
9 жыл бұрын
John smith *meow
@renalynramos5509
2 жыл бұрын
•How to find the slope of the tangent to each curve when x has the indicated value. • how to find the equation of the tangent line to each curve when x has a given value
@faizahanif9515
5 жыл бұрын
what about the curves whose equations are not given.....i had a curve that said y=f(x) thats it and it was curve not a straight line
@griftorifto2
12 жыл бұрын
Thanks man, I totally forgot about this comment. One year on and I got the Mathematics award for my whole school. I think he just inspired me to be passionate about maths
@lizzyberg1082
4 жыл бұрын
I dont know why but his way of talking is so off topic or distracted I quickly lose attention
@kevinimmanuel8036
8 жыл бұрын
Why are we using the limit ?
@reetasingh1679
8 жыл бұрын
We do it so that the gap h gets smaller and smaller and when h becomes 0 then the points x and x+h coincide, or in other words they become the same point and the line through that point becomes the tangent
@PsychoHF
12 жыл бұрын
@vaccumenhancer439 That makes absolutely no sense and is the worst attempt at a math joke I have ever seen. Congratulations.
@Tomwenn
14 жыл бұрын
@teakz89 He, is just calculating out the equation. (3 x deltax)^2 is (3 x deltax)(3 x deltax) = 9 + 6 delta x + delta x ^2
@Jayy1903
14 жыл бұрын
Ok... Im not learning calculus yet.. but it seems so confusing... lol slope slope slope slope.... im like :O
@tmoo8779
8 ай бұрын
why does my calc book make this look like actual rocket science
@zae4398
12 жыл бұрын
@Aitsu58 because the square of a number is it times itself so it would be (Dx X Dx)/Dx thus giving you Dx
@ShynyMagikarp
12 жыл бұрын
@SuperXD25 check out the website khanacademy. It's INCREDIBLE. Helps me out with school so much.
@blackbeltjr
11 жыл бұрын
Anyone else a 9th grader in geometry watching, and understanding this? No? Well crap.....
@sarahbostrom9358
5 жыл бұрын
Maybe someone can help me out here. If we make delta x arbitrarily small, and we have to divide by delta x to find the limit, why does the limit not become arbitrarily large?
@ChololateRain123
12 жыл бұрын
In a way, but it's just a fancier way of saying "the slope of a point on a curve."
@MuslimAlchemy
10 жыл бұрын
It seems this video cannot be viewed from within the Khanacademy site, ecxept in Bangla.
@sufyanali8820
7 жыл бұрын
sir u explained very well and i learned now what is slope and derivative, but please tell me in geometrical meaning of derivative why ∂x=dx but ∂y≠dy? plzz
@uhaperson
13 жыл бұрын
The two people who dislike this video got an F on their math report card!
@zinalpatel1449
7 жыл бұрын
THANK YOU!!! I know understand the calculus EC that my algebra 2 teacher gave us! There's no need of a tutor when ya got Khan Academy :))
@winterine4827
4 жыл бұрын
This was released on my birthday and I find it a bit coincidental that I'm watching this now
@ChololateRain123
12 жыл бұрын
So the formula that he derived for the slope of the secant line was f(x + dx) - f(x) / dx. In this particular problem, he said that x would be 3. Since f(x) is x^2, we can plug in the function and variables. So the formula becomes (3 + dx)^2 - (3^2) /dx. We can simplify the (3+dx)^2 part into 9+6(dx) + dx^2 by multiplying it across. and the 3^2 into 9. Now what we have is: 9+6(dx) + dx^2 - 9 all divided by dx. The 9 and -9 cancel, leaving with us 6(dx) + dx^2 / dx ==> 6 + dx. Hope this helps.
@ChololateRain123
12 жыл бұрын
Well because if he made it the limit as x --> 3 or 2, then that would be finding the slope of the SECANT line. So what he wants to do is make that distance between both points -- delta x -- minimal, so he make it zero. This give him the slope of the TANGENT line, which is basically the linear slope that is just exactly touching the point on the curve he wants to find the slope of. Hope this helps.
@sudhagupta4488
7 жыл бұрын
does taking a derivative of function each time means we are taking its slope???
@david0aloha
14 жыл бұрын
@Yvesiscool It is, you're correct. Because he didn't take the general slope algebraically - he took it at x=3 - he got the derivative at that point (rather than the general derivative for all points which would be 2x). x=3 || 2x = 2(3) = 6
@ChololateRain123
12 жыл бұрын
What's even more amazing is that that is his handwriting on a computer! I mean, in real life on pencil and paper I'd say my handwriting is mediocre. But when I use paint or a drawing pad, my handwriting turns to crud. I wonder what his REAL handwriting looks like...:P
@elladette8840
4 жыл бұрын
Isn’t 6 + delta x squared and not 6 + delta x
@TheBull06
14 жыл бұрын
lol its crazy how your name is sal, mine is too, everytime you say your name i get startled haha. thanks for the great videos, youve helped verify my choice of math as my major.
@reggiefields6551
7 жыл бұрын
thanks. ive seen several of your video series now and they are always helpful. you are a great teacher
@dinkylicous1234
14 жыл бұрын
great work, you dont know what a difference you are making to this world. you have pioneered a new form of learning in a much easier and much more understandable way. you sal should be knighted for your time and effort you are giving to the world. you are a generous man who gives up your valueable time to help people whom you dont even know. great work again. from all youtube fans.
@JesusPacheco
12 жыл бұрын
There should be a whole semester of calculus in KZitem...... pfff classrooms?? forget about it. I just need to watch this guy!
@valentinacalivano8436
11 жыл бұрын
I wish you could do the whole course of Calculus 1 !! you are waaaaaaaaaaaaaaaaaaaaay better than my professor !!! :/
@1matth3w1
14 жыл бұрын
Respond to this video... i love you man. your vids are percise, accurate and easy to understand.. i understood everything
@johnmitchell6283
6 жыл бұрын
I'm in the freakin fettle position right now...……..
@ellipszia
9 жыл бұрын
thank you very much khan for taught me this way of thinking!
@ehwarrior
10 жыл бұрын
Thank you for these videos! Now I understand the section we are going over much more than before.
@mrthuvi1
14 жыл бұрын
@Iislunatic We don't exactly divide by zero there. It's the limit of the slope when delta x approach 0.
@ronaldshing5110
5 жыл бұрын
where did 6 delta x come from?
@JohnnyRedzin
13 жыл бұрын
@ViniciusFiocco Because when this: (6h+h^2)/h Can be reduced to this: (6h/h) + (h^2/h) The h's then cancel out and you get 6+h
@jiansuniyo1234
13 жыл бұрын
one of the best videos superbbbbbbbbbbbbbbbb!!!!!!! gr8 video really veryyyyyyyyyy helpful
@interstateruler
12 жыл бұрын
How did you got the 6 delta x?
@sdgfsdg75
10 жыл бұрын
6dx + (dx) ^2 / dx / by dx and u get 6 + dx over 1
@RomanNumural9
10 жыл бұрын
When something is divided by 1 you don't have to write it. 4/1 is still 4. 6 +dx/1 is the same as saying 6+dx
@corytung
13 жыл бұрын
ur voice is as calming as morgan freeman's
@masseffected20
11 жыл бұрын
@iTreasons I failed calculus in high school. I did good in Trig and algebra. I went to college and studied physics. I ended up with a 3.8 GPA. I am trying to get a Masters in Physics with a concentration in quantum mechanics and particle physics. I am coming back to Calculus for personnel reasons. Unless you become a math major or engineer you don't need to completely understand calc. Like someone stated, just worry about GPA my friend, and breath... you'll be fine.
@Sameen_The_Business_Coach
2 күн бұрын
Nice bruh My calculus is also much bad And I'm trying harder to improve it at university level so I may gain a good gpa at the end of semester 😊
@MrMoeqt
11 жыл бұрын
dude i love your vids, theres a spot in heaven for you
@shaddyhamster3969
3 жыл бұрын
You just blew my mind
@theBurningice31
9 жыл бұрын
why is the second y-value squared? it wasn't in the general formula above
@Aeonilluminated
9 жыл бұрын
David Yen The function of x is f(x^2) or y=x^2, so the first x value (3) translates to 9 for the corresponding y value because 3^2 is 9. The second x value 3+h must also be squared to find the second y value corresponding with it: hence (3+h)^2. I hope this answered your question.
@KoolioJosh
11 жыл бұрын
dat moment when the stuff your prof finally teaches is beyond the khan academy vids, Fuuuuuu!
@Sameen_The_Business_Coach
2 күн бұрын
Good job sir 👍🏻
@pieyouel
13 жыл бұрын
Sal, you never know how much joy you bring to all students all over the world! (including me) ^^
@TheKilodaneko
6 жыл бұрын
Wow this was incredibly useful!
@therealjordiano
13 жыл бұрын
Man this is awesome, so easy to understand :D this guy should get paid
@Pancake833
7 жыл бұрын
omg this is absolutely beautiful, i love math =')
@GFauxPas
13 жыл бұрын
@DarklightALBANIA Δx is just a variable, if I give you a function of x f(x) = 6 + x then f(1) = 7 If I say f(Δx) = 6 + Δx Then f(1) = 7, does that help?
@pulkit5352
Жыл бұрын
Thank you very much
@saptarshisahoo5075
9 жыл бұрын
As i tell "present when needed most".Thanks
@GermanSnipe14
11 жыл бұрын
@blackbeltjr it's really not too hard to understand as he explains everything he does step by step. Good job but don't get too big of an ego
@vaibhavnayel
12 жыл бұрын
so derivative is the same as slope?
@griefer1
13 жыл бұрын
...and i need to go to college why?
@unisbushra
14 жыл бұрын
thanks so much man , your efforts are surely great and for good sake too.
@msven
12 жыл бұрын
Wow....I feel like a nerd that I just laughed at that for about 10 seconds.
@TheMostHigh13
4 жыл бұрын
You're awesome, bro.
@adrimu2007
12 жыл бұрын
OMG i understand EVERYTHING NOW!!!! Thank you so much! I feel like a genius or something, haha.
@mar8014
11 жыл бұрын
Mr Khan, thanks for reaching out to the young and hopeless. You'r awesome.
@Rabidbluejay1
12 жыл бұрын
KZitem education is amazing lol
@reggiejax
12 жыл бұрын
this might be a dumb question, but if you set delta X to 0 doesn't that mean you had a 0 in the denominator earlier in the problem? isn't that meant to be off limits?
@paritoshagarwal8840
6 жыл бұрын
John Wilkes Booth if you're still looking for the answer watch the earlier limits videos
@david52875
13 жыл бұрын
@vaccumenhancer439 Get over it
@Samcx9
11 жыл бұрын
The day Khan Academy is in 4k is the day I will die!! :D
@MJfullofGrace
11 жыл бұрын
yeah, in my understanding the "delta x" is just a variable in this equation.. isn't it? so you just have to copy it when adding, correct me if i'm wrong.
@r4fa3l59
4 жыл бұрын
∆x is "variation of x" "∆" means "variation"
@ChinatownDragonKC
11 жыл бұрын
Search up the FOIL method
@jairoselin5119
3 жыл бұрын
Sir, how many tangent lines does a point on a curve has?
@maryamlina644
3 жыл бұрын
It has only one tangent line i guess as it is one point only
@jairoselin5119
3 жыл бұрын
@@maryamlina644 why not there s more than one?
@maryamlina644
3 жыл бұрын
@@jairoselin5119 cuz we are studying the slope of the curve at that particular point which means that we need only one tangent line 🤷♀️
@jairoselin5119
3 жыл бұрын
@@maryamlina644 you're rgt.. but am asking how can you say that ua tangent is unique?
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