Understanding the Definition of the Derivative

[trevormovestuff]

This was very clear.  Thank you!

[The221618aa]

LONG LIVE patrick!

[BarksRosaRota]

I heard the work derivative for the first time today. I have no idea of what it is, can someone help me?

[deborahrez12]

Amazing!!!!!!! Thank you very much!!

[ShakkIsLife]

Why is it lim h -> 0?

[patrickJMT]

@ShakkIsLife if h -->0, the points get closer together

[Asteretsa]

So, basically, you're trying to find the value of the gradient of the secant closest to that of the tangent, to find the gradient of the curve at the point, am I right? :S

[060296rules]

the one my school uses is

f'(x)=(a*x)x^x-1

so for example:

f(x)=12x^3

f'(x)=(12*3)x^3-1

f(x)=36x^2

are these the same?

[tkdman45]

as difficulty -> ∞, my love for you -> ∞.

[patrickJMT]

@tkdman45 lol

[Iced0826]

College math has decreased in difficulty thanks to your videos. I'm now ahead in the discussions. Thank you x infinity! :">

[patrickJMT]

@Iced0826 wonderful : )

[troylockheart]

Im taking up my college lessons ryt now and ur helping me alot man ! ^:)^

[riamykeil]

you should win the Nobel Prize. Honestly, you're amazing -Thank you soooo much! (by the way, I love the way you say "exAmple" lol)

[ajoutram]

mwalimu nzuri sana

[Tinalb26]

Thank you sooooo much! You have no idea how much this has helped me! My math teacher just told us how to plug in numbers to the equation, but now I know what it means! Thank you!!

[patrickJMT]

@Tinalb26 understanding is always nice :  )

[XxCrAzYAzNxX4]

duuuuuuuuuuuuuuuuuuuuudee.....­... props

[StrawberryMarshmalow]

I wish I had your as my maths teacher!

I'm finally beginning to understand derivatives and limits!

[patrickJMT]

@StrawberryMarshmalow keep watching! : )

[steverock85]

I will never look at the rollercoster the same way :/

[x3Heroiinex3]

so why this sataniqu star LOL :D

[SpacySpaceCadet]

Thank you thank you. I stared at my calc book for about two hours, very very helpful. I think you may save me for my calc test.tuesday!

[ejsg34]

thank you! patric!!

you saved my life!

My professor couldn`t explain the definition of derivative clearly like you!

[VegasBabeXOXO]

you sir, are a God!

[virtuosoikingpin]

I finally found someone who is better at teaching math than Sal, from khanacademy. It looks like I won't have to try to understand the hieroglyphic filled nonsense that is a calculus textbook. Do they not realize that the chapters are useless if they make it incomprehensible and leave out half the steps to do the problem? Anyways, thanks for being awesome, and probably saving my scholarship by keeping me from failing calculus.

[theantiantichrist]

This is how maths, and everything else for that matter, should be taught. Understanding the reasons, and mechanisms behind things is crucial to getting students interested, and giving them a proper understanding of what they are learning. Modern schooling is just about packing information into brains. We're wasting so many minds.

[golferb0y7]

great video thanks!

[natash179]

WOW, you're awesomeee, couldn't ask for a better explanation. Thank you!

[falconpally]

this video is awesome thanks for the sharing your knowledge

[patrickJMT]

@falconpally any time!

[DatVideoChannel213]

Your videos have been a great help! Thank you so much!

[ccg1994]

finally someone tells me WHY this is the formula, not just "this is the formula, memorize it & use it to find the derivative"

Thank you sooooooo much!!

[patrickJMT]

@ccg1994 understanding > memorizing!

[CristinaPeter411]

Thank you so much for this! I stink at math and I have been watching your videos consistently to help with my homework because your explanations are so much more clear than my professor's and you have helped me drastically. You are so much appreciated!

[patrickJMT]

@CristinaPeter411 happy to help! : ) tons of calculus stuff, so visit often and tell your friends!!

[EricMarinelli]

You are an amazing, amazing person. While my teacher isn't bad, I wish my teacher taught as well as you! I totally got it the first time I watched it.

[jeanblaaa]

Lol omg I love you. Today we had the sane lecture but it was so confusing and the scetch was huh?? But yours was sooo easier to understand. Please put more up of calc vids!

[coketita1992]

Yes, you are a super star :)

[seifdeiab]

GOOOOD! JOOOOB!

[FincayraMerlin]

Thank you so much; I really like knowing the "why" behind formulas. 

[otownfever]

Im gonna send a link of this video to my Math professor with the subject: How to teach derivatives. Thanks Patrick! Everything makes sense now. Why go to class.

[1PinkGiraffe1]

Thank you so so so much.

[circlesarecrazy]

You are awesome. :D

[The22Macbeth]

best math tutor ever!

[IEatNubs6]

Let me see if i got this right. So as Delta "x" tends to zero of the secant line, we end up with the tangent line by finding delta "y" over Delta "x"! FINALLY, SOMETHING FROM MY MATH BOOK MAKES SENSE!!! XD

[sapphire776]

Patrick, Patrick. You might just be my hero for the next 7 weeks. Business Calculus is the only thing standing between me and my Associate in Business degree. I work office hours so I have to take it online. The course only provides sporadic videos so it's pretty much interpreting the text on my own. I failed pre-calc doing it that way, but I didn't know about your videos then. Thanks for doing these! Your explanations are so easy to understand.

[kjeersten]

Wow... you really brought it all together for me... thanks!

[dsephobe]

gosh it's brilliant!!!!u bravo...the teachers never tell the definitions, they ask us to recite all time. & memorizing things always mess me up. thx Jesus that u made this great job!

[terranewb1]

Why don't they just tell us that!!

[qualquan]

A double game is usually played with the value of h. We must agree that h in the denominator cannot be zero. Yet in the final quotient it is made zero to get an exact answer. So which is it? Is h nonzero or zero? It cannot be both just to suit our fancy. There has to be consistency otherwise it is intellectually unsatisfying. I have my own explanation where h remains nonzero all the time yet we get an exact answer such as derivative of x^2 = 2x (exact). Not enough space to elaborate.

[manwithgills]

Thank you so much. This helps me understand the equation versus memorization to regurgitate this for an exam.

[WHY70122]

This explains everything that fucks me up this whole semester...

[NanSings21]

you're a life saver!

you're the reason i aced my calculus exam!

THANK YOU!

dont stop making videos :):):)

[theAcidBlues]

This is a bit confusing. My teacher uses delta x instead of h :S

[GenieInAFantaBottle]

omfg youtube, more adds?

[sweetred02]

Great explanation!!!

[victor82784]

so no matter what the value of h it will get smaller

good explanation!

[baersenn]

thanks from sweden, hopefully I will nail my test tomorrow now :)

[rajupaapu]

Great explanation!!! Now I don't have to cram that formula.

But, I have a basic question - to find the slope of the tangent line (which is a straight line) why can't we use the equation y=mx+c? We can always extrapolate the tangent line and find the coordinates and hence the slope.

[AlwaysBeMyThunder21]

You have no idea how much you've helped me understand my calculus homework!

Don't know if you actually read you're comments but I just want to say THANK YOU!

[naturelle711]

you are genius!!!!

dude u make this much more simple

thats just pure awesomeeenesss !! <3

[k1ngross]

Brilliant explanation. :)

[1904home]

Awesome. Making sense.... imagine that in Calculus!!!! It was just mindless plug and chug for me in college... but this is an amazing explanation. Thank you. One thing i did not get was the 'zero' at the end.. could you please clear up why you wanted to get h as close to '0' as possible? Would you not want h to be almost the value of x, i.e., that val, x, does not look like zero on the graph. Or is X zero on the graph? Thank You.

[coolikas]

@1904home I think the h only represents distance from the point x and not a specific point on the graph. That's why it approaches 0, not x.

[kar453]

@1904home i think he means that he's trying to get the second point as close to the first point as possible. so if h is almost zero, the second x coordinate will be very close to the first x coordinate, making the points very very close. the actual value of the coordinate isn't zero. h is almost zero, not x. so yeah. okay i sound dumb for saying this.

[FuneralMarky]

Thanks I understood it on the first sitting, if only my school teacher was like this.

[Fish51992]

Can you please come and teach my calc class?

[shanipost]

You r a rockstar or mathstar.

[theMDWiz]

love your videos our teacher quizzes us and gives us homework on derivatives and such and we are stuck on unit circle lol. Your videos make it so much better

[bpatte191]

Thank you so much for the helpful video!!! You make math exponentially easier to get a grasp on with your great explanations and examples! :D

[jayboyfloyd]

thanks very helpful i might have to watch it a few times again, but it definitly helped

[patrickJMT]

@jayboyfloyd glad it helped. if you get it the first time, then i am a super star

[MrSharkyful]

@patrickJMT I got it first time:-)

You are helping so much with this, I have already finished college but some things still aren't clear...

This is much better way to learn than to read some definitions that doesn't even understand the one that wrote them ...

[DeadScream92]

@patrickJMT Hey! I got it the first time and I watched it at 1 a.m :))... guess you are a super star :P.

Btw...I can not thank you enough for these videos.

Best wishes

[assassin465]

@patrickJMT i got it the first time and my teacher hasn't even taught it yet. so your a super star lol

[bobsterwald]

Yay! patrickJMT, you are awesome :D Thanks :D

[icdp]

haha nice video. Im going to engineering school next semester, gotta know that lol

[VictorAndScience]

İs this video the same that 'What is a Derivative? Understanding the Definition' I'm following all your videos on your site. And that one is not working...

[patrickJMT]

@VictorAndScience yes, it is the same

[mypinkdollprincess]

You make the most complicated stuff in math..a piece of cake for me!! Thanks for being truly awesome!

love,

mypinkdollprincess aka your #1 fan! lol (:(:

[patrickJMT]

@mypinkdollprincess hahaha, thanks #1 fan!

[3kazuko]

U rock my socks! U're just awesome!

[ztifnz]

Great video, thanks

[AwesomeNstuff]

Oh wait now i understand what your trying to accomplish :)

[toiletweener69]

dont do x's like that lol. but excellent video! :] thanks

[rodrigomlp17]

keep doing this great job

thank u from Brazil :)

[GeneralGergles]

Thank You!

[lauraiznow]

sooooooooooooooooo helpful :) Pretty much made my day.

[bessady]

awesome... It took my teacher a month and a half to go over the chapter, and at the end,, not even a single student understood his explanation or method. Just ten minutes made clear what i could not understand in six weeks....Thanks

[hhkk2222]

thanks! :)

[RichEddie84]

You are God of Math. And you will inherit the earth!

[NovaEX1]

Hey i would like to ask, what are the conditions for a derivative to not exist? There are some conditions to be met before it can exist right? Can you enlighten me on that?

[markiss92]

you saved my butt, my teachers threw this at me and now i finally get it

[ColorsMercurial]

Your videos are so useful! I'm taking AP Calc BC at my high school and I listen to the lesson in class, but don't entirely understand. When I watch these videos afterwards, I can understand the topics better. This is especially true for conceptual concepts like this one. Thanks!

[soul24rage]

@ColorsMercurial lol same. why can't there be more patricks....

[jahchyn]

This is the best explanation I ever had! You should definitely be the math professor of my university!

[mehwish56]

very excellant explanation ...........

[Matsuyama1234]

Dude, Patrick, this explanation is so clear and perfect. Now rather than having to memorize a bland formula, I can always think back to what exactly it means when trying to remember it.

You're awesome. Don't stop making videos.

[patrickJMT]

@Matsuyama1234 glad u like it: : )

[alexwhb122]

This is awesome! thank you. I finely understand how the derivative actually works.

[ValleLucas]

Good enough.

[Mejiera12]

Finally this is starting to make sense. Thank you. Thats the best explanation I ever heard.

[apatternforu]

This is a pretty sick demo, love it! So I'm graduating this year and I'm taking Real Analysis 2. Suddenly everything got fucked up defining a derivative in R^n---->R^m LoLoL, we all freaked out. Guys like us need to be teaching though, I hope you have a job. Are you Pure, Applied... you sound like a Pure guy like me.

[patrickJMT]

i am nothing, i do not do math research

[nickschor]

Where were you 30 years ago when I really needed you!!! Either I got a lot smarter over the years, or math educators have gotten much better. Thank you very much. Math ROCKS!

[patrickJMT]

i was probably still not able to walk or talk yet...

[fateater77777]

"so what do you do in ure free time" "I make educational math videos" "...."

[ohjaysus28]

Great Vids... Thanks so much

[sullivanseven]

Your new videos are much clearer and have better lights :)

The material is still amazing though

thanks

[Giorgetti31]

My understanding got smaller and smaller and smaller and smaller and smaller and smaller. Hence making me closer and closer and closer to crying.

[MIT2004]

what is it that you are not understanding, seems pretty simple to understand. Ask i will answer

[streetkleena]

God, your making calculus for me so much easier for me. THANK YOU!

[MunchVids]

I know, I've learned most of what I know about calculus in the las two days since I discovered these videos.

[darkxsociety]

I'm taking a calculus class via distance ed, and I can't explain how much these videos have helped me understand fundamental concepts that my textbook has just kind of skipped over, as if to suggest I should just somehow intuitively 'get it' by myself.

Anyway, rant aside, thank you very much!

[FractalDistortion]

There is nothing better than having someone explain a concept in a clear fashion. This is good for engineering as well!

[panefuldeath]

kinda slow, but still really cool.

[eeenihs]

This is so clear.

makes so so much sense.

[shadowC10ne]

Thanks for the video. Learning math without understanding usually leads to confusion.

[2273897]

dude u r awesomness

[blackdefender]

....i really thought that the place you're writing at is a piece of paper...until you erased what you wrote.....anyway, I understood the lesson more after I was reviewed by your video so Thanks a lot!

[egyprincess10]

hi, your videos are awesome and i was wondering if you could make more calculus videos im taking it as a dual enrollment class :)

[damianwba]

I don't konw why is it that I understand this if I've watch/listened to your video in EN but if someone explains this thing to me in my language I'll get everything mixtup... anyway tnx for the vids JMT

[BrainTrapped]

Thanks!

[IntegratedDerivative]

I have that exact same ruler! Thanks for the video :D

Maybe I'll watch all of them to brush up on my calculus for the upcoming quarter

[Keroma03]

Thanks for all the videos!

You should do more proofs like this. It works much better understanding stuff then memorizing formulas for everything.

[btkw]

i finally understand this... thanks