Calculus: Derivatives 2.5 (new HD version)

[SuperMpepper]

@Andy8Tran

Yup, I definitely thought something like that too when he said graze. high5 for sexual innuendos.

[Andy8Tran]

I'd like to graze YOUR curve ;)

[HostingReviews1]

wow.. these video make it easy.. thanks

[ShadowLink678]

I can't believe it simplified down to just 2x. Haha.

[ohmyarmelle]

I logged in to say I love you, and why aren't you my college math teacher? Lol

[chinotovar]

wow this is awesome!! u make me calculus so easy :)

[phillysports266]

my professor makes this seem like rocket science...this video makes it seem easy.

[CapnKeys]

how do I reach these kids?

[MementoMario]

@theendjr Ah, I know what you're getting at now. Yes, there are simplified rules to find out the derivate of a function in a heartbeat, however, those rules come from the method explained in this video.

[RizwanSaid]

i owe u my academic life man, thanks

[1extenderpro]

Thanks for the formula.

[theendjr]

alright i got this stuff now and compared it what we are doing in class, our way is easier, there is bascially rules which tell us Y=X^2, Y1=2X and other rules that help us find a general form of finding the slope without going through all the stuff he did at the start of the video

[EpicTwinkler]

Ah, that's good but here we need to give answers without shortcuts. y=x^2 is supposed to go through the long process. :(

[DarklightALBANIA]

I am looking forward at math in 3D ,oh the limits is gonna be right in my face

[machomacho69]

@jozmaz. It may be a bit confusing to switch between deltaX and h, but realistically the world won't accommodate your needs. Sal is exposing two common uses, is it so hard to grasp a small variable change? Do you get angry when f(x) is represented as g(x) too?

[sidar87]

@machomacho69

Don't be an elite about it. Many people do find it confusing if they don't keep variables the same, because it looks like something else/new ( while it isn't) to the previous videos.

You get it, that's great but don't reflect your state of knowledge/intellect on others. It's arrogant. Everyone learns at their own pace and speed.

[noor121212121212]

Sal bhai...You are the best...I think i want to major in math just because of you...jk...but seriously, your the best. Thanks.

[jozmaz]

it would be a lot less confusing if you didn't keep hopping between h and delta x

[newDAVIDnew]

m for slope...

I love ur logic (:

[eyeamon]

Thank You so very much I FINALLY understand ... now to start calculating instantaneous velocity and acceleration!

[MrVargasesteban]

beautiful

[SharxKL]

I get this now! You explain so well! Thank you!

[JLchevz]

7:31 "this is a big result!! this is EXITING" hahahahahaha

[thatonetom]

"that wasn't tangent enough for me" lol

[Nadrealis]

I've never learned so much in such little time. I've literally learned more from you than any teacher I've had in high school. Amazing.

Subbed.

[MrEatinurfoodz]

Very very helpful in learning. I decided to try to learn calculus as an independent activity outside of school, and these videos are the most user and learner freindly i have seen yet. I thank you greatly for a job well done.

[supercalifragilismic]

is there any videos of sal giving general tips about studying or reviewing for an exam.. what he usually do.. etc

[koketka69]

YOU ARE THE BEST!!!!! Great explanation, and it is so pleasant listening to you!

[timidemerald]

OH MY GOD IT MAKES SENSE!!

[hammd123]

PLEASE HELP: When i see the video it feels that i am understanding but when i try to repeat it at my own i start missing links and logics. What should I do? I normally do not take notes during the video, i just try to understand then try to repeat at my note book. Is my method of understanding wrong? PLEASE HELP I AM IN DEADLY NEED OF UNDERSTANDING LIMITS AND DERIVATIVES.

[vanmojo23]

@hammd123 When it comes to finding limits for the most part all you do is just replace the variable with the number that it is approaching. For example, if you take the limit as x approaches 2, you replace x with 2.

Me personally, when I'm finding derivatives I just use the different rules like the Product Rule, Quotient Rule, etc. It will give you the same result as the method that Sal is using in this vid. I hope this helps.

[hammd123]

@vanmojo23 Thanks alot and yes i agree that using derivatives rules make things pretty clear and easy. I was worried because when i try to teach or share LIMITS or DERIVATIVES with my friends I feel uncomfortable with the way i proceed towards the solution. I think I need more and more practice. Anyway, Thanks for your guidance.

[vanmojo23]

@hammd123 No problem. And good luck! :)

[kimjaemin1035]

@hammd123 nb

[bigfinlessbrown]

I'm not gay, but I love Khan.

[MAGICgunPs3]

CAN YOU MAKE A TUTORIAL ON BOW TO MULTYPLIEE?

[JLchevz]

This is greaaaaaaaaaaaaaaaaaaaaaat!!!!­!!! my life is complete.

[xXSparky117Xx]

Mathematics is mind-blowing.

[daggermail1]

7:41 minus 2x? isn;t the curve y=x^2 not as wide?

[LyriiczBoii]

@daggermail1 I think the minus sign you see is meant to be an equals sign.

[Luckier8]

@daggermail1 it's an equals sign, not a minus.

[daggermail1]

7:41 minus 2x?

[beary605]

There is a really easy way of figuring out deriatives. ax^n--anx^(n-1)

[jt11347]

great video, really learned a lot. Thanks!

[corksmusic1]

You really helped me by taking it that bit further and asking, 'but what does that mean?!' Thanks.

[Onisasu]

amazing video!

I like the colours you choose~ haha!

Thanks for all the help!

[ananaszjoe]

Good video quality, terrible audio quality.

[KamakazieKat]

"If I put an apple there it'd be apple squared"

[diegoarriaga123]

IN SOVIET RUSSIA, LIMIT FINDS YOU!

[yasinege]

@diegoarriaga123anothers all in germany

[rudyk1008]

thanks very much!

[whydizz]

apple squared ha ha

[Boscotrips]

IIIII GOT IT.

[mahlatsemankgele]

Great vid!!!

[tardfarms]

extremely helpful thank you

[chexican09]

The HD looks so clean, amazing, and easy to read. You should remake all of your Calc videos Sal! Lol

[1073601]

whoa, thanks for the help

[Tenshiwing]

so here i am, 2 weeks from a major maths exam, finally understanding derivatives. I just learned the general formulas for all the major functions and never really quite understood what a derivative is. And I studied derivatives 2 years ago. I can't emphasize enough how much you're helping, Sal. And I also can't stress enough how much I appreciate your effort that you've put into this.

Thanks! And keep at it, you're doing an amazing job.

peace :D

[UdontnomeYGO]

WOW i'm in 7th grade and i actually get this!!!!! My teacher thinks giving tons of homework will make you magically get it and giving tests every 2 days will make you get higher grades.....

[chexican09]

@UdontnomeYGO Woah you're in 7th grade and you're learning this?? What are teachers teaching children these days....

[KirkenesVGS]

thx Sal, your voice fits perfectly on these videos

[idster7]

Question: At 5:57, with the slope of the secant ((x+h)^2-x^2)/h, why wouldn't you plug in 0 for h there to get the derivative? That would give x^2-x^2=0 slope. How is it possible that by simplifying, you change the value of the answer? And how do you know where to stop simplifying?

[elpuna]

@idster7 if you plug in 0 for h at that point, you have a zero in the denominator and numerator, making it undefined. What you thus need to do is factor out the "h" after multiplying out the (x+h)^2, removing the h in the denominator, allowing you to plug 0 in for h.

[idster7]

Question: At 5:57,with the slope of the secant: ((x+h) squared - x squared) over h, why wouldn't you, when attempting to find the tangent line, place 0 for h at that point? The answer then would give x squared minus x squared=no slope. How is it possible that by simplifying, you would actually change the value of the answer? And how do you know when to stop simplifying?

[pitupraveen]

@idster7

I have the same doubt.......

"how do you know when to stop simplifying?"

[nikanj]

I remeber learning all the rules of calculus in high school but never recalled deriving it. I'm getting a small sense of how Newton or Leibniz felt when they figured it out.

[trombona89]

HD looks good Sal!

[crazymun13]

I'm SO EXCITED!

[xecut10n3r]

this makes so much sense! AND IM NOT EVEN TAKING CALCULUS!!!

[Quinstol]

Sal, thanks for these videos, they've been helpful and I wish I'd found them sooner.

If you continue to update your calculus series, I have one small suggestion: mix it up a bit more with the examples you do in future derivative videos ... toss in some radicals, do stuff like e^(4x*cosx), use letters to represent constants and explain how to identify them as such, etc. The derivative series you've got up now seems like it has 4-5 videos of very small variations on the same problem.

[Najma202]

Jouleano: Your easier rule is not that easy if I am not getting what you just wrote, so leave it for the experts to teach us and leave your .02 cents at home, thanks!

[Jouleano]

There is an easier way to take the derivative of a curve. Using something called the Power Rule, which is essentially this:

If F(x) = ax^b, then F1(x) = (b)(ax)^(b-1),

(Where b is the exponent and a is the coefficient of X.)

Which can then be proved by F(x) = X^2, and F1(x) = 2X.

[timtu22]

I think he is teaching the intuition between rules like that.

[timtu22]

behind*

[infinitylol315]

there are also many more, constant rule, constant multiplication rule, sum & difference rule, product rule, quotient rule, and the general power rule

[Quinstol]

It does indeed make it much easier to crunch out derivatives, but it's not a great tool for illustrating what a derivative is and getting comfortable with the idea. Given that limits and derivatives are core concepts in calculus, I think it's good when teachers linger on those things for a bit before introducing the derivative formulas.

[alitou001]

@Jouleano yes you are right,but Sal is trying to give the concept then if you watch his next videos,He will show constant multiple rule and the power rule you have mentioned,thanks anyway.

[mistryman112]

Thank you so much! You explain it so well :)

[weso548]

bad writing?? SaL is the King of writing! lolz.. most of the time..

[banditdk]

07:18 what happens to 3th h

[alitou001]

@banditdk check his videos about limits and you will understand it.

[rewtguy]

2x + h as h approaches 0 would be 2x + 0 or 2x.

[mlionel32]

Wonderful! You are doing a great job man, very, explicit and comprehensive! My prof simply jumps at answers!

[kingsnacker]

This guy is awesome!

[travwg33]

your vids are great

[urumqilik]

keep them coming bro ...really enjoying it except the bad writing :-) you are doing something good for all and thanks for your help .

[hpsfl]

Beggars can't be choosers ^^