Calculus: Derivatives 2

[BrokenSound92]

i gots an exam in an hour. YOU ARE MY HERO.

[devilnight911]

simply, you are way better than my professor 

[professorquack]

awesome great easy to understand lesson that's interesting as we never know what marker you are going to use, lol.

[TheYellowochre]

i'm a sentient mass of cosmic radiation and i understand this!

[sweetblackstarx]

i have i big math test tomorrow... wish me luck : D

[eriann20]

THANK YOU VERY MUCH! I hope that sums up how thankful I am for this! You made me understand this better than my book! I have a report which is supposed to be based on the book, and now I get how -f(x) randomly appears on the solution :) Thanks again!

[jangoonpants]

Doesn't it simplify down to 6 + h, not 6 + h^2?

[gonnwall]

@jangoonpants actually it does

[viacalvy]

@jangoonpants yeah, that's what i got. i think either way though the answer is the same.

[BreAveryAsh09]

8:30 "what does this tell us? what have we done for ourselves?" LOL. haha. nice vids! very helpful.

[martystreets]

Khan ur the best man really love u man helping out engineering student

[nemojuanowski]

wow you're explaining hours of reading in 10 minutes. Thank you so much for saving me from pulling all nighters

[JJK1996]

Lol I'm a Finnish ninth grader and I actually understand this. Pretty well done mate! :)

[TerminatorToast]

So for the limit part of this problem/example, the slope is 6 because (simply) h is equal to zero at (3,9) and the slope is h+6? Therefore, 0+6=6?

[H0oLIgAnSsRo0lMaRrSz]

@ToXiCvEliXiR that's what I thought! did u ever find out y it wasnt?

[strangerhythm]

Awesome, he's like the Bob Ross of Calculus

[platazar]

WHAT IS THE NAME OF THIS SOFTWARE? PLEASE.

[Nitrocroc]

I wish I found this BEFORE my chapter test. Oops. Thank you for saving my grade in calculus, not including first quarter

[mosow09]

how do u get 6h in ( 3 + h) ^2 - 9??????????????? thats the only part that confused me, Please respond maybe im not seeing smthng obvious????

[chowchio]

@mosow09 expanding (a+b)^2 = a^2+2ab+b^2... so a=3 and b=h

[mosow09]

@chowchio Thanks bro

[sheaofleaves124]

@chowchio Question: Does this also apply to (a + b)^3, or is that a completely different story?

[TheLoveformankind]

confusing

[EpicAlbert69]

you are making my teacher jealous lol, u teach better than him =D good job mate keep up the good work i'm 15 yr old and i know calculus so tyvm

[DEEEKAYify]

Why do i have to learn this on youtube! I am paying a fortune to my univ

[ToXiCvEliXiR]

shouldnt the result be lim_h->0 (6+h) and not 6+h^2???

[jawade42]

These few derivative video's have helped me in 20 minutes as much as 5 weeks of class. Thank you.

[Arabian1Princess]

My future loves you so very much

[Zigzag263]

Is there an even easier way to do this? like a formula or something?

[tematapeak1]

@Zigzag263 there is, the simplified formula for an individual term is: nx^(n-1), so to derive: x^2+x+1would be: 2x^1+1

[KannonLax]

I love you.

[CaribbeanAC]

I actually like math now.

[famousto0]

why does (3 + h) 2(squared) equal 9+6h and not 9+h2 (squared)? Where does he get the 6?? PLEASE HELP!!!

[OneChance99]

@famousto0 google the FOIL method. its a way to factor (3+h)^2

[gunsnbam]

@famousto0 Because (3+h)2(squared) is NOT (3*squared* + h*squared*). It is (3+h) * (3+h). The little number 2 does not mean multiply everything inside by 2. It means that there are two (3+h) side by side. Its called the FOIL method and you end up multiplying every number by every number. Google the "FOIL method".

[94Dalguy]

@liyajohnsphilip I think he means why did he write 6+h^2 when it was actually 6+h.

[94Dalguy]

@j3fford h^2/h=h^(2-1)=h^1=h

[cml4456]

Anybody else think this is fun?

[radwizard916]

@cml4456 I do!! And I just started calculus :) :D

[2495romit]

super cool way of teaching! and on top of that teaching sooo well! thanks a lot

[J3fford]

Isnt it 6+h rather than 6+h^2? please clarify.

[liyajohnsphilip]

@J3fford yes it is 6+h

(6h+h^2)/h = h(6+h) /h n the h cancels out n 6+h is what is remaining.

[JewHeffna]

thank you ...... many times

[LizziesAnswers]

YOUUU are saving me from SOO many emotional breakdowns!

[ImUrFanGirl]

There is a simplier way to solve this equation:

Coeffient*exponent^ exponent - 1

for the first problem x^2 u will get 2x ( because coeffient 1* eponent 2= 2 and for the exponent value 2-1 =1 or x raised to the first)

from there plug in the x value of 3 in the derivative (2x) and the answer is 6

[TheBuschline]

MATHEMATICAL ERROR @ 3:57:

You cannot divide the polynomial in the numerator by h.

I believe the correct way to solve would be to FACTOR h from 6h+h^2

you would have

h(6+h)/h and so the h's would cancel and you would end up with 6+h.

[joselrico1]

I think there is something wrong.... I got different result following an example from the book of calculus

[Darkrunner1975]

@strikemewiththunder

Ah ok. So it's just 6/1 because you don't have a specific real world application to solve (what is the slope in inches, centimeters, miles). So the slope is 6/1, but what increments of measurement that might be will be dependent on what you are measuring?

[jdurnal]

your getting too many positive comments like oh my god! amazing.. i just wanted to say that your an alright teacher. and thank you

[SUpeRzAp16]

7 people are going to hell

[Darkrunner1975]

I like watching your vids, but I was wondering what the slope is. You said six. What is the measurement of 'six'? Six what? Whatever you decide to plug into it? Six inches? Six feet? Six meters?

My math teacher was marking the days until he could retire. And I hated him.

I understand how you got there, but what is it measuring?

[holumyde1]

xcuse me but i have a problem with this. is the change in x and change in y the same that u just gave all the change a common 'h'? the h in the denominator is change in x and the h on top is change in y but a learner wont be able to differentiate that. so i just want to know if they are the same. thnx

[cincitymenace]

I'm only in trig right now and won't be taking calc till next fall, but I fully understand this stuff! Thanks a lot!!

[nooremuhammad]

great u are outstanding.........

[prcntm]

Aahhhhhhh... "Eureka" moment! This is awesome.

[RobSchneeberger]

you explain it better than my calculus professor he didnt even give us the graphing approach to the problem before diving into all the algebra

wtf

[GlobalNotes]

@ 4 min, wouldn't you get 6+h?

if you factor the "h" out of 6h+h squared--> h(6+h)/h

please clarify that for me. Thanks

[Light1c3]

At 4:20 you said (6h+h^2)/(h) = 6 + h ? how ?

[Corefang]

@Light1c3

6h+h^2 / h

You factorize it to: h(6+h) / h

The 'h' then cancels out eachother and you are left with: 6+h

[The0Peach0Technique]

its so ridiculous to me that when i wanted to cram for my final in calc that i at 10 pm went the hail Mary route and youtubed "how to do calculus" and found a video that completely explained in 20 minutes what my teacher could not

[markmason2k8]

you could just do dy/dx and then input your x value to get the gradient of the curve at that point

[Clipster15]

I'm starting a calc class tomorrow, I'm scared. :O

[barrettski189]

"Ahhh.. I need to get another tool..." :D

you are awesome! Your vids are really helpful!

[dieraupe2]

epic fail h^2 :P

but anyways your tutorials do really help

[soloohk]

These series of tutorial are so great, clear and concise.

Thank so much for your sharing !

[xconfigure]

around 3:40, u said (3+h)^2 is simplified to 9+6h....i get the 9 part, but how did u get 6h? wouldnt it be 9+h^2?

[aBangProduction]

@xconfigure nope, the general formula for squaring brackets is:

(x+a)(x+a) = (x+a)^2

= x^2+ 2ax + a^2

where the (3+h)^2 was squared, 6h = 2ax, where a = 3 and x = h

[MsGrammarnazi]

Your tools are fine; don't worry.

[damnitslukky]

can you just explain that last part of the equation were (6+h). I'm not in calculus yet bet this is easy for me to understand so far.

[coldnitee]

I guess 7 people missed the Like button and accidentally hit the Dislike button (Y) (:

[verzilx]

LAwlzzzzz h^2 hahahaha funny :D

[unown17]

Dude, that is sick. I'm in Mechanical Engineering and I had no idea I could do things like this. I used to just memorize these things.

[ShygirlUsername]

Seriously. Thank you so much...I wish my Calc teacher in college broke it down as simply as you did here. Bravo!!

[cdnmr]

After 7 three hour lectures I was more confused than when I started. Watched first 2 derivative vids and it makes sense.

Love the sloppy graphs...look exactly like my chicken scratches!

I have already emailed some classmates to check your vids out ! Thanks

[lena11sandy]

@cdnmr  do u do maths in college

[Raidenv]

Hi at 6.59 where you try and find the derivative of f(x+h)-f(x)/h should it not be f(x+h)^2 as your x coordinate was x+h and the y coordinate should simply be (x+h)^2 as dictated by the function.

[pgh5002]

Don't you love it when head slapper mistakes don't effect the outcome of the problem.

[micher43]

At 7:34, how did you get 2xh???? Ahhh, thts bugging the crap outta me! hahah ur a very great teacher tho, I just finished 7th grade and the way you teach this, it makes total sense!! lol

[Valentino319]

how come at 3:14 it becomes 6h? shouldnt it be 9+h^2-9?

[micher43]

@Valentino319 i'm stuck on tht too cuz at the end he does the same weird simplifying...i think it's like the exponenet number times whats in parentheses?? idkkk

[Valentino319]

@micher43 I think he multiplied the (3+h)^2 coz that gives:

(3+h)(3+h)

9+3h+3h+h^2

9+6h+h^2

[micher43]

@Valentino319 thank you....i totally forgot about that

[pgh5002]

@micher43 (x+h)^2 is the same as (x+h)(x+h)

(x+h) is a binomial

In this case [(x+h)(x+h)] you have multiplication of two binomials.

To multiply two binomials you have to use the FOIL method.

(x+h)(x+h)

(x)(x)+(x)(h)+(h)(x)+(h)(h)

x^2+xh+xh+h^2

x^2+2xh+h^2

[micher43]

@pgh5002 Thank you for clairifying that..lol i get it now

[spilloholiker]

what program does he use?

[NilsMcCloud]

If this was taught this way at every high school, we'd have a lot more mathematicians & physicists @ the universities. Keep up the good work ;)

[GolKol91]

it should not be h square! It should be 6 + h only!

[MartyMarts187]

freakin genius!

[mirandakoofficial]

You are an amazing math teacher - going to lectures and going over my notes didnt help as much as you!

[mak3myda3]

Yeah. I dont get it. I'll just stick with Trig :D

[joshuachukahei]

thank you very much!

[mbn129]

Thank you was lost and now found!! Many year middle school teacher - first time calc student!!! Have a calc for teachers class and felt totally stupid - like I should get this fast!!! But the high school teachers make the pace so fast!! Thank you for helping me understand this!

[Xoxocube]

i followed this untill.... 3+h squared minus 3.

What is the 3 called? Why is three used...

In the same way (3+h) squared -9 .... your just using the x and y axis values in there.

Oh man abstract. I hate math... but ill keep trying.

[StevenK2121]

Amazing job of teaching, and so much cheaper than getting a tutor

[Luckyxseven]

*Suscribe*

[PuzzleCentral]

Small mistake. You said 6h+h^2/h was 6+h^2, when it actually is 6+h. In the end it didn't matter because h=0. Great videos though. Really helpful.

[Xoxocube]

@PuzzleCentral Yeh i got lost there. 9+6h... squared right? Theres an extra plus h squared in there.

Does Khan redo video's if they have mistakes?

[HowToDo92]

dauummnnnn...this is soo sikk..i just started calculus and i already know whts going on. thank you soo much!!

[Sectorsophia]

Why can't my teacher do this well? She should be in politics, with her amazing gift of being able to talk for hours without saying anything.

[Parabol0086]

@Sectorsophia Hahaha. That's awesome. They all seem to have that in common.

[TheJunoclub]

khan!

recently i have studed ur lecture.

i 'll give u a better tool to easily write.

please leave a message.

[datCRUNKbuay]

Khan i hope you see this!! But i love what you are doing and want you to know that if i am ever successful i will be donating a fair portion to you and your fantastic cause!

[eriqire1997]

makes algebra look pretty stupid

I'm 13 and I should be taking calculus

[peretz125]

@eriqire1997 soorry but no u shuld not, stop being cocky and live through simple math

[eversmann85]

This is much better than what I learn in polytechnic and university. Thanks.

[ftkmnm]

wow... im a freshman and i can understand this

[walkingreject86]

same here. I'm 14 and this makes perfect sense.

[algeiranall]

this is ok but seriously he needs to get his facts straight-still, made it a lot clearer for me!

[KLHKathie1010]

it's so kewl..it helps me alot on my hw..thanks. =]

[darklordsma]

Thank you so much~!~!!

[karlkarlkarl1234]

yeah it is pretty nifty

[ScanGun]

Where did the 6h in the numerator come from @ 3:13

[w1nd12]

i got the same problem scangun. Can someone tell me where the 6h came from?

[rgrewal04]

(3+h)(3+h) when you foil it...it becomes 9+3h+3h+h^2= 9+6h+h^2

[ScanGun]

thanks alot.

[ftkmnm]

thank you!

[2glam4aUsername]

lol you forgot to distribute out the h at the end.

In 6h+h^2, you distribute out one h. and get h(6+h) all divided by the h in the denominator. The h in the denominator cancels out with the distributed out h and you are left with 6+h.

ha, I guess I learned something in class after all

[TheEliteNinja]

factor out one h*

distributing would be the other way around

h(6 + h) ---distribute--> 6h + h^2

[TheEliteNinja]

sorry, commented before i saw the video lol.

[2glam4aUsername]

it's called a mistake. Copying what I said and changing one word doesn't make you any smarter.

[Bullwiggit]

2LAME4aUsername, more like.

[2glam4aUsername]

What? I try to help future videos and I'm suddenly "lame"?Ohhh because I said "distri bute" instead of factor?? Jeezus Chrise.

Why'd you reply to me twice? I guess multitasking is hard. Don't worry, you'll soon perfect sucking cock and watching calc videos simultaneously soon enough. Bitch.

[hector0282]

YOU ARE TOTALLY CORRECT, the guy in this video needs to simplify more.

[bebe2ful]

wow, all you have to do is take the 2 down and mult it by 2 and you get three...........so much simple!!!!!! you reallly dnt have to use that formula to get 6, if the teacher doesnt ask you

[goevenu]

so u get slope 6 from the coordinates by substracting 3 from 9 easily...

[terstenfatiha]

thank u!!!

[Gohgoroth]

The only problem, which at this point is irrelevant, the most common notation for h is actualy Delta X( the little triangle)

[fahddoggz]

gorgoroth? my god, thats some evil music, i had a friend who listened to taht, he was a satanist freak.

[Gohgoroth]

I love Death Metal, I have been listening to it sence I was 6 years old, for personal reasons. And You really should understand what Satanism is before you call someone who follows it a 'freak'. There are a few different versions of it, and Levayian(sp) Satanism is a Agnostic religion, Devil worship is completely different. Just realize that the Christian Church and all of its branches have popularized that idea that Satanism is a bad thing, even though it really is not anti-christian at all.

[kingofdice66]

may Satan be with you mi child, and kill you at the end

[Gohgoroth]

Satan isn't a deity at all, Satan is symbolic for hte answers in yourself. more often then not, when you are thinking about something it is because you already know the material, you you are trying to retrieve it. That place you are trying to retrieve it from, the part of you that is a record of all of your knowlage and experience that you can't ever fully tap into at any one time, that is what Satan is symbolic for. It isn't evil, it isn't cruel. there is no magic or hate or sacrifice...

[fahddoggz]

so the slope of the tangent line at x=3 is 6? so we are moving down from 3+H, as in h goes down and we get the slope of six at the exact point of x=3. i see...

[fahddoggz]

as H approaches 0, h is 6.....ok this is where i get stuck, im not understanding how this limit thing is working, that h approaches 0 it becomes 6.

[Nutterbutterz95]

Well, H is just some generic variable he applied to denote that some generic change to x happened to make f(x+h). Applying the slope formula to that gives you the slope of the secant (passes through two points) line. You don't want the secant line slope, though, because that's an approximation. You want the slope as h (that generic variable) approaches 0, which will give us the slope at exactly whatever that point is.

[fahddoggz]

ya so h is the displacement from x, and when h becomes zero, we have the slop of x at a, the instantaneous rate, or the derivative right?

[Nutterbutterz95]

Yeah. You've got it.

[Thymonico]

f(x) becomes 6 when h approached 0... ;)

[jibooie]

Wow, how relaxed, simplistic and wonderful this is to have for a reference....and it's free...thank you so much

[AkimotoMichiyo1428]

OMG, can please and be CALCULUS BC TEACHER PLEASE?!!! my teacher is REALLY CONFUSING. you did great

[rainman8367]

you're a genius! thank you.

[datguy729]

you should be a teacher, if ur not already one

[TheChadZomg]

how did u get the 6h?

[stepperman06]

when you have a (constant + variable)^2

Ex: (3 + h)^2

1.) you square the constant: 3^2= 9

2.) double the constant and multiply it by the variable: 2(3)(h)= 6h

3.) you square the variable: h^2

(3+h)^2= 9+6h+h^2

[roller0coaster0gal]

this is nice =D

[mimib1230]

Perfect explanation! I missed 3 days of class due to flu and now I think I am better off than if I hadn't missed...because otherwise I wouldn't have seeked this out!

[Crouton351]

How do you know that the limit of 6 + h is 6?

[roller0coaster0gal]

because u have the find the limit as X approaches 0, so u set h to 0, which would make 6+h, 6

[GutZ105]

Not exactly sure but from what I gather when you reach the h ----> 0 you would have 6 +h = 6 + 0 ---> 6

[MakubixZero]

hmm.....he needs a tablet pc lol

[MakubixZero]

my bad...if he is using a tablet pc....he needs another

[Dreamland2100]

i was17,i finally know about the d/dx x^3 = x3x^2

n(x^n-1)

and how the d law come from:[f(x+h)-f(x)] / [x+h-x}].

i aim physics and math throughout my study.

i think science is the best,and thank alot!

[nanaceceful]

um... im so confused!!!!!!!!!!!!

[Spjungen]

Wonderful, but indeed, that h^2 instead of h would be a big mistake in any serious instance. Luckily it's an instructioinal video, everyone makes mistakes, and your comprehensive method of teaching makes up for the error, in my opinion.

Cheers.

[ilovepink8915]

wow really wonderful

[sitiaminah1980]

great explaination!!!!

[Ykoahi]

writing and working along with you = winnn

I'm starting BC calc this year and I want to get a head start!

[Zetrax3]

Great teaching. Thanks.

[enjoyablesounds]

the slope is 6 ..degrees?

[DeifyReality]

If you have an equation like y = 6x + 1, it would have the slope 6.

The slope is kind of the steepness of a line.

[enjoyablesounds]

I understand that the slope is just a number..and the bigger this number is, the more steep the actual slope is..wouldn't it be neat , since every tangent line CAN be described in degrees..you could create a direct connection between the calculation of derivative aswell as the amount of degrees after evaluation on that specific point? anyway confusing ..i just wanted o achieve a better understanding of actual outcome of the "prime" of the function..