Calculus: Derivatives 2 (new HD version)

[interstateruler]

How did you got the 6 delta x?

[TheFirstPyromaniac]

@bebefore3

[PlayNChilllStudio]

YAY HD

[SuperXD25]

Biology, Chemistry, Math... this guy's a freaking genius!

[Dreadlord67]

@SuperXD25 check out the website khanacademy. It's INCREDIBLE. Helps me out with school so much.

[SuperXD25]

@Dreadlord67 do you mean the channel our a website?

[vaccumenhancer439]

Put this video in a equation like (yx+) 3/5 powered by 4+ axis + _ xgetalife+ 12 =? +5 = then youll have that sucking pussy problem solved in a () + x see?

[lost4468yt]

@vaccumenhancer439 You should be a maths teacher.

[MegaNalak]

@vaccumenhancer439 this guys gonna pull up next to you in a ferrari in 5 years and you're going shake a maccas cup at him while desperately trying to articulate the words "I'm hungry".

[david52875]

@vaccumenhancer439 Get over it

[PsychoHF]

@vaccumenhancer439 That makes absolutely no sense and is the worst attempt at a math joke I have ever seen. Congratulations.

[DarklightALBANIA]

I understood everything but what is that slope you said ex 6+delta x for ex delta x equals 1 and it is 7 ,what does that 7 mean,What it is apples oranges ,so I don't get what that exact number really is exactly

[GFauxPas]

@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?

[wakaboomnick]

thankyou so much for your videos, I learn so much from you

[Danterod329]

in my university the professor is just 240p :(

[504omni]

@Danterod329 haha

[TUY3TNHUNG]

I love sal

[broadwaybound1000]

OOOOOOH Now it all makes sense......

[CdL3o]

THANK YOU

haha I'm teaching myself AP Calc BC

you at least explain things much better than what I come up with :)

yay home schooling!!!

[vvoops]

i literally dick around in AP Calculus Class now, and come home and watch this. THIS IS MY MATH CLASS :D

[corytung]

ur voice is as calming as morgan freeman's



[theaidantomkins]

loooooove you.

[ViniciusFiocco]

why 6 + change in X ?

6:26

I didn't understand...

[JohnnyRedzin]

@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

[crowman131]

HD =0

[therealjordiano]

Man this is awesome, so easy to understand :D this guy should get paid

[uhaperson]

The two people who dislike this video got an F on their math report card!

[paulceltics]

great

[griefer1]

...and i need to go to college why?

[vincentpersichetti]

I have never, in my life, taken any calculus EVER. I now understand derivatives b/c of this video alone. Simply Amazing!

[jiansuniyo1234]

one of the best videos superbbbbbbbbbbbbbbbb!!!!!!! gr8 video

really veryyyyyyyyyy helpful

[scuzzulus]

nice. i am only four years old and i understand. i bet anyone who doesn't understand feels super dumb after reading this. ha - HA

[pieyouel]

Sal, you never know how much joy you bring to all students all over the world! (including me) ^^

[Wreaksauce]

ALL THESE FORMULAS MAKE PERFECT SENSE NOW!! :D

[LtimeburnerL]

hd's are good...

[VFB1210]

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.

[lhagenable]

@VFB1210 thank you

[hadassah356]

I can't begin to tell you what a great help you are! You're videos are extremely user friendly and very helpful. THANKS!

[RonBurgundy161]

Where does the 6 come from before the deltax?

[cxrodformrx]

Thank you so much for taking the time to redo your older videos in HD!.

[jonathanmaximebrun]

Thank you so much, I always used to be in the normal in my math prog and since I discovored ur videos i'm always something like 10-20 prct over the normal, great explication, great demonstration, your doing a truly nice job, thks again!

[griftorifto2]

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.

[Gursha88]

brilliant. very well explained.

[mitomke]

Hey I wish I had a teacher like you years ago

[ithejuggernaut]

He should get a new application that enables him to draw better. :P

[smikemc09]

the derivative is f'(x) = 2x he needs to not do this its stupid

[kurozaki45]

so the slope of the secant was 6+ delta x and the tangent line is the limit as delta x goes to 0 right?

[thephantom1228]

my brain hurts....

[Iislunatic]

I can see it all works out but h was set to zero at the end and was also the denominator. Can someone explain why dividing by zero is allowed? Otherwise, completely understandable =D

[mrthuvi1]

@Iislunatic We don't exactly divide by zero there. It's the limit of the slope when delta x approach 0.

[gundamnoober5]

@Jayy1903: time x changes, so does y, and vice versa.

[gundamnoober5]

@Jayy1903: hey, im in grade 10, but im doing calculus because apparently im smart, even though i think im not. remember, slope is just y=mx+b, slope being mx, but remember rise over run. In point slope form, you use y1 and x1, but where does that come from. When you get 2 pairs of coordinates, you label them x1, y1, x2 and y2. Things like f(a) are just variables that represent the numbers we need, meaning literally f of a, which we use to find slpe. When he says change in x, it just means every

[unisbushra]

thanks so much man , your efforts are surely great and for good sake too.

[dinkylicous1234]

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.

[dinkylicous1234]

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 .

[rexirexi]

a lot better than my class for which I paid $4000

[1matth3w1]

Respond to this video...  i love you man. your vids are percise, accurate and easy to understand.. i understood everything

[Jayy1903]

Ok... Im not learning calculus yet.. but it seems so confusing... lol slope slope slope slope.... im like :O

[glittergrl24]

Assuming the following: Derivatives 2 > You

[blessednhm]

You are a Godsend! Thanks a million!

[RHCPchaosMAYHEM]

Excellent teacher! and its free! why the hell am i paying for college again?

[Yvesiscool]

isn't the derivative of x^2 =2x?

[david0aloha]

@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

[Matrik44]

Amazing! everything is so clearly explained. I'm definitely going to be looking at all of your calculus videos! Thank you soooo much!

[teakz89]

still dont know where he got 6 from? how can 6 be from being squared?

[Tomwenn]

@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

[Mifty123]

i got problems with this material for years i took classes and nothing now i understandd 10xxx alot

[mohegansoon]

Sal, Could you please explain how you get the curve of the x^2 Thanks

[vetruven]

i wish every of your videos were HD :( it looks SO much better, well it still helps a ton - Thanks Sal

[TheBull06]

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.

[orelhai]

sal rox

[prakashltpm]

Excellent Videos. Keep up the good work.

[weso548]

Thanks again Sal! These HD videos are great!