Finding a Derivative Using the Definition of a Derivative

[MAILIAMMUSIC]

freakin commercials :(

[patrickJMT]

@MAILIAMMUSIC commercials pay for all the free stuff you watch on youtube

[FoolishTheMortal]

Why is this formula the same as the formula for the difference quotient?

[patrickJMT]

@FoolishTheMortal well, it is not the same cause this has a limit. : ) but part of the reason you see the difference quotient in algebra is because the person who writes the book knows it is important in calculus. the difference quotient helps us to approximate the slope of the tangent line by finding the slope of a secant line; we then take the limit of these slopes to get the slope of the tangent!

[laiklang]

This gonna save my life in college!!

Thank you, sir!! :)

[hotstuffwatcher]

got a 2 day AP calculus B/C test tomorrow and friday. ur vids rly helped me out. thank you!

[cutiecool32]

you're awesomeee

[aggceed719]

Omg, thank yoouuuu calc final in 10 hours!! DX

[LopsidedCircle]

i can't find the other examples on your site :(

[nickschor]

Thank you, Patrick!!! Is this another expression of the quotient rule?

[kickit246]

I can't believe you posted this video back in 2008 and your still active on it! Its almost been 4 years... I'm glad though :)

PS - Calc final in 2 days, 26 minutes :(

[patrickJMT]

@kickit246 good luck! : )

[ian559fresno]

@kickit246 I feel bad for you.

[kickit246]

@ian559fresno Thanks man... I feel pretty bad too... lol :(

[morganlazar33]

I know that this a simple and silly thing to ask but can you quickly explain how to multiple out (x+h)^3? My Pre-Calc teacher taught us a simple way to do it last year but I can't remember now and it takes so much time on a test to do it out the long way! Thanks, you rock!

[patrickJMT]

@morganlazar33 binomial theorem

[patrickJMT]

@morganlazar33 and pascals triangle

[eviladam1993]

@morganlazar33 try product rule. u=x^3, u'=3x^2, v=(x+h), v'=1. I think u can manage from now on ;)

[MrJasonekos]

@morganlazar33 (x+h)(x^2 - xh + h^2) or x^3 + 3x^2h + 3xh^2 + h^3, is that what you were looking for?

[iiottoii]

sub + 1

[NUMBERTWOHATER]

why did I watch this AFTER the test =='

[patrickJMT]

@NUMBERTWOHATER tons of calc stuff for your future needs ; )

[dontdependonearth3]

youre a machine! thats impressive, thanks for the upload=)

[patrickJMT]

@dontdependonearth3 i am a luv machine (blonde redhead)

[amasayspfft]

@patrickJMT blonde redhead? this automatically makes you so much more awesome.. maybe the most awesome person ever. it must feel great that you're helping out tens/hundreds of thousands of students :D

[patrickJMT]

@amasayspfft yes, it does feel good : )

[enokenful]

Thank you so much for the assistance, the help is very much appreciated! sub +1! :)

[patrickJMT]

@enokenful glad i could help! thanks for subscribing!!

[compendiumcharlie]

Oh my gosh! I needed this on a test and I had no idea what it even meant! thanks this video has been really helpful!

[MrKnnknn]

If I understood what you are explaining, I wouldn't need to watch this video in the first place, in other words you are explaining what you are doing, but you're not explaining why you're doing it. What is h? What does it represent? You don't explain that. Thanks for the video anyways.

[patrickJMT]

@MrKnnknn maybe you should watch the video ' understanding the definition of a derivative ' instead of whining about this one. thanks anyways.

[Betterthanyou1234561]

Can anybody help me out at the step 6:00 about those h s

[dtbjjrb]

@Betterthanyou1234561 After he cancels the h's, he plugs in 0 for h, and simplifies. That's why they seem to disappear.

[Juands10]

how do i find the derivative of the derivative?please helpppp!

[patrickJMT]

@Juands10 you just take the derivative of the derivative. do what i do in this video, twice.

[Juands10]

@patrickJMT thanks sir! I really appreciate your help ;) thanks for responding

[anikazangel1]

do you do any videos where you use the second definition of the derivative?

[patrickJMT]

@anikazangel1 no, i think this is the only one i use

[emayne50]

Are you a turor in the california are or is there a way i can email you questions that i am having problems with



[patrickJMT]

@emayne50 no and no

[SuckmyErsela19]

My savior for calculus :D

[TheAnvilMan]

I love you

[awefilledcreep]

thank you for your videos so much

i feel my urge to kick puppies after calculus class subsiding.

[rosiecouture1]

Thank you so much for your videos...I have my biggest/most important maths exam of the year coming up in a few weeks and your videos are really helping me consolidate and revise everything :)

[VegasBabeXOXO]

omg... where have you been all my life! you have saved my grade

[solidiquis1]

I hate ugly algebra

[srednaslenoloc]

you're the best. I was home from school today with a cold and my teacher is going to be sooo surprised when I'm answering questions tomorrow! Thanks Again!

[AlexShelden]

What's this short way everyone keeps bringing up?

[againstmesellout]

if f(x)=x^2+x would the derivative not exist?

[SLIMmcGlinn]

@againstmesellout The derivative would be 2x+1. You gotta do the math or use the shortcut though.

[2YMCMB2]

PatrickJMT for president

[patrickJMT]

@2YMCMB2 president is the last thing i would want to be. either you being called a liberal hippy do good-er or a racist republican dick cheney butt kisser. people are nutz when it comes to politics, i for sure do not to be a target for assassination. i think ill just keep quietly making my math videos ; )

[cynthiaaknox1]

@patrickJMT uh, yeah... no. But thank you for the videos.. much appreciated.

[patrickJMT]

@2YMCMB2 thanks for what i assume is love though : ) 

[jojogirl2008]

thank you so much! I really appreciate you and your videos!

[KingpinMalc]

Could you explain how to use the derivative to find an equation for the tangent line?

[patrickJMT]

@KingpinMalc i have videos exactly on that if you do a search on my videos

[CurryBiskit]

im watching your videos and I have a calc test in two hours (:

[patrickJMT]

@CurryBiskit good luck! one hour to go!!

[ccg1994]

I got my first A on a math test because of you. Thank you so much for all of your help! :)

[BorealNeal]

why do people on you tube teach better than actual profs??

[XboxPwner94]

i really wish i had a math teacher like you, would make math so much easier

[hotfusion0]

i love you.

[GodzOFWars]

Ah you just managed to make it in my subscribed list :)

[genalinda3]

Well my friend, your gonna teach me calc this year (even tho this topic is part of pre calc) :) where have you been all my 3 weeks of school? I think I might not fail my quiz tuesday after all :)

btw. you have a really cool voice. :P

[patrickJMT]

@genalinda3 i have been right here.. where have YOU been? : )

[TheGreatGoomba5]

you are my guardian angel (: 

[skatexius]

Not only are you great at explaining but your voice also calms me down and somehow it gets me into "lets do math" mode. So, even if i do already know how to solve such problems, I just cant help myself but to watch at least one of your vids or art least have it as "background music" while solving :)

[patrickJMT]

@skatexius always happy to help out someone that likes the stranglers (good for you!)

[8644371]

PatrickJMT... disgracing poor math teachers everywhere.

Keep on keeping on!

[patrickJMT]

@8644371 no, not at all! there are tons of great, hardworking teachers out there. (and some a bit less so!)

[8644371]

@patrickJMT lol I'm referring only to the poor math teachers.

[jayr11jayr]

why do i get it when you're explaining but when its my teacher explaining, i don't really understand much of it. you're cool! :D

[patrickJMT]

@jayr11jayr i guess i am a good ' explainer ' : )

[Cancer98765]

I was watching one of your vids earlier this year in math class on my ipod and the people near me ended up moving closer as opposed to listening and taking notes from the teacher. Needless to say she got pissed and sent me up to do a problem she deemed "difficult". To bad it was one you had just done in said video =)

[patrickJMT]

@Cancer98765 hahahah, sweet : ) in your face pissed off teacher!

[The22Macbeth]

@patrickJMT you're amazing math teacher i hate those who dislikes your videos

keep uploading excellent videos! wish you the best!

[reuben024]

sir thanks for ur help im goin 2 approach my test tomorrow hope this would help :)

[Ladarzak]

My favourite word in math is now "tedious" because it's so much better than "frustrating enough to make me cry."

[MAT0R0]

Phuck! This is totally easier way than the teacher does it! Damn it! I SHOULD OF FOUND THIS VIDEO EARLIER! I failed my 2 tests! ='(

[defiantHipHop]

I was hoping you were going to do one like f(x)= (x+1)^1/2 :(

[alreadytakenthe3rd]

Ugh. I've been watching your calc videos this year in preparation for AP Calculus in the fall and I'm not looking forward to doing this stuff, since now I know how to use the shortcuts.

[TheRichardChu]

What about

1/x^2 ? cause im trying to work that out and its turning into a big mess for me =\

[FuNnYmOjOoO]

whats the difference between the two formulas and when do u know which one to use?

[denden528]

wow



[Systemscai]

Pat lemme tell you i had this math teacher in mid. school that ruined math for me, math was my favorite subject i loved it and i was good at it. She fucked it up for me, i went from being Valedictorian in Mid. school to struggling throughout High school with a 70 something average. If You had been there instead of her, no joke i know i would of been in an IVY league School. Cuz of that bitch i saw teachers and the school system in a whole other light.Keep doing what u doing bro, we all love you.

[8mariarichiez8]

You have saved my ass this semester...=)

[kinghenrikm]

dude thank you and for also explaining it so thoroughly really helped out

[MorenaMuneca]

Thank you.

[Kim5291993]

i wish there was a little version of you i could carry into my math class with me!!

[WongeneKIM]

I enjoyed this video! :) Thank you~

[DirtyTriks]

When you begin @ 6:18, how did you get rid off "h" in the equation of (t+h+1)(t+1) to become (t+1)(t+1)?

[cadmusdixon92]

@DirtyTriks He did (t+0+1)(t+1), which simplifies to (t+1)(t+1) or (t+1)^2

[DirtyTriks]

When you begin @ 6:18, how did you get rid off "h" in the equation of (t+h+1)(t+1)?

[glitchnoise]

woahh..i thought calculus was a different world...just realized it its pretty much algebra dressed up ready to go to a party.

[TASIARAYESkl]

Date an Asian lady lushfmlk.info

[SmokerTJ]

in my test they asked to use the definition of a derivate to show a certain f(x) is differentiable at 0. How...?

[patrickJMT]

@Teflon718Don good luck!!

[MrPiPPo]

dude, If I ever meet you in person, I'll buy you a sharpie of your choice.

[kddc4479]

I wish you were my best friend in high school. :O

and by that I mean rival >:]

[patrickJMT]

@kddc4479 i skipped most of my senior year, so i am not sure how much of a 'rival' i could be in anything!

[kddc4479]

@patrickJMT xD Well because I had no one to be some sort of motivation I basically slacked off TT___TT

[terrygrada]

@kddc4479 I wonder how many best friends you have... lol

[pendolly]

marry me patrick.....*sigh*

[patrickJMT]

@pendolly ha!

[jackxzx]

patrickJMT

firstly, thank you for the video its very helpfull.

by any chance do you have a video of Notations of derivative?

i can't seem to find it Or maybe its called something else?

[jackxzx]

bro, i'm sorry but i love you!

[mongoose308]

Hey, what school (University or College) did you go to?

Lol, you should be a professor or teacher. :)

[labatymo]

OMG! I spent hours reading text books trying to figure this out, and all i had to do is watch this video

[allensine]

First and foremost, thank you so much for taking the time to create and post all of these videos! I have a completely unintelligible textbook for this course and if it weren't for your explanations and examples I would be lost!

The link on patrickjmt "What is a derivative? Understanding the definition" does not work. I get the mechanics, but am unclear as to why and how they work - how exactly is a derivative different from a limit (or is it)? Thanks again - you're amazing!

[allensine]

@allensine After searching through youtube and not finding the link to "understanding the definition", lo and behold like magic as soon as I admitted defeat it appeared! Great video with great explanation (as always)! Thanks again!

[1904home]

very cool. been out of school for 10 yrs now and i'm going back to school for a BS in Math and so i am just studying up online before I get into my Calc for the first time in a long time. Is it just me or has the internet just exploded with knowledge in helping folks learn topics like derivatives and limits? I mean, it is absolutely crazy. I can get online and learn from a dozen teachers the same topic. Back in the day, it was just you and your teacher and if he/she wasn't any good, oh well!

[PERSONAfan01]

i was stumped on this but when i watch this it all came into perspective and i was able to do my work THANK YOU!!!!!!!!!!!!! SUB SUB SUB

[treflip063]

amazing <3

[chbobcats20]

Thank you for your videos, especially from limits to this video, it has made a night of trying to understand a chapter's worth of test material much easier and shorter.

[itachi8282]

your a lefty.

[ScootRodgers]

I was thinking about dropping calculus until I found your videos. You're a live saver

[bossbower]

You're a lifesaver!

[BreakneckWalrus]

I don't understand how anyone can dislike your videos! Through one watch of your video I understood the principles behind volumes of revolution, and my class is still just on definite integrals (which, by the way, I also used your videos for. Brilliant!).

I'd always been fuzzy on the limit definition of a derivative (mainly because I transferred into Calc AB after my class had finished limits!), so I've been using your videos to catch up. Keep it up! :D

[JimmyStartinStrength]

i didn't take calculus in high school but I am required to take this calculus course in university for my program and you're really helping me out alot, THANKS! :)

[haterofannoyances]

i dont know you personally but i love the fact that you put videos up that are more educational than my professors. you = awesome!

[Szeania08]

Very helpful, thanks. d (ʘ‿ʘ) b

[gibri]

thank god for the quotient rule

[fengie]

for the 5 people that disliked this, go jump off a bridge

[patrickJMT]

@fengie ha, well, maybe that is a bit extreme : )

[mypinkdollprincess]

@patrickJMT regarding your reply to 5 dislikes: You're such an inspiration!! ROCK ON!! <3

P.S. How in the world did I forget to wish you a happy new year? Hope 2011 has been great for you so far...best wishes and love,

mypinkdollprinces <3

[patrickJMT]

@mypinkdollprincess happy new year to you too! things are so far, so good! i hope the world is also treating you well.

[1904home]

@patrickJMT - it all comes with the package when you have fans!!!

[BassDJB]

@fengie Hahaha, the 5 people that disliked the video are math teachers that cannot teach.

[nustylez]

@fengie maybe they should... then we can apply what we just learned today :D

[74SteveG]

@fengie lol, Patrick is cool as hell

[mrpig89]

so,,, if you had an equation like x^2 + 2 or some random constant at the end. Would you pretty much be able to cancel it out when you take the derivative since the derivative of a constant is 0?... If that makes sense xD

[mikemondays]

@mrpig89 As long as you get 2x for the derivative of x^2 + 2, then you're correct.

[TheBaseballman1990]

this makes much more sense than how my teacher shows us. i can not only read what you write, but you actually know what you are talking about, which is pretty essential when it comes to math. thank you so much!

[malikannas786]

i just cant understand last 2 steps......! why did you apply limit in 2nd exmple why not in 1st example????

[XxGreenTundraxX]

What if you're given x? As in 3x + 1 x=1

[rachelleBOO]

You are good, my friend! Thanks for helping me out! :)

[xcstacy2]

I have a problem that I just can't get. I need to find the derivative of the function X^4+X^3-40 where X=C and C=-3. Your website seems to be down and I didn't know your email and couldn't send a msg via you tube because it's set to only friends can mail you. please assist, much appreciated videos btw.

[PlatonicPhi]

how did he get (t+1)^2 at the end? shouldn't it be (t+1)(t + h + 1). the h flipped caneled the one on top not the one in t +h +1 which it can't that i know of.

[snowhazel]

@PlatonicPhi He substituted h=0, hence why it's not included in the end.

[bvlgary09]

I'm curious, what benefit would you have if you know the derivative? Why do we want to find the derivative?

[Bleachnarutoawesome]

@bvlgary09 If the graph is position vs time. The derivative would be the instantaneous velocity. If it's velocity vs time, the derivative would be the instantaneous acceleration.

[Bazil]

I have two different calc text books, neither of them bother to show the steps that you do.I spent two hours trying to understand what they were doing in the steps they did not feel the need to show/explain; thank you for showing how exactly this is done.

<3

[hastyincubus]

Thank you for your vids! They’re really helping me in my AP Calc AB class. Without you, I would’ve dropped out a while ago!

[cosm0]

I love you :) (no homo) thanks!

[jimmy0629]

awesome dude

[unoob9882]

you are a life saver

[krislu719]

thats totally helpful!　Thanx!!　BTW whats ur email?

[krislu719]

that's totally helpful!!! i totally mass that up on my calculus class!!

BTW whats ur email?

[AnonymousJuan]

Did you know that I just answered one of my test questions with the help of this video? Many thanks bro!!! You're gooood!

[Corrup7edChaos]

I learn math so much more from you than any other math teacher. thanks :)

[patrickJMT]

@Corrup7edChaos u r very welcome!

[hungryhamburger]

im feeling some bromance for you

[ApacheGolfer]

I understand the way you set up the equation when you are only given f(x), but what do you do when you are given f(x) and an x.

For example, how would you set up the equation when a question asks for the derivative when f(x)=x^3 at x=-2?

[ohhgeeme]

I learn more from your 7-12 min videos than i do in my two hour calculus class.

thanks.

[StupidSpoge]

Thanks!

I have my final tomorrow...

These types of problems have been bonus questions on every quiz and test, and I never bothered to learn them... haha They're easier than I thought!

I owe you one.

[djzapz]

Thanks for this. Final tomorrow and I didn't remember exactly how to do these.

[TheCj383]

wow. impressive thank a lot!!!!!!!!

[Oron999]

Oh my, you've been a lovely help. I've got my AP Calc BC exam next week, and we conveniently haven't covered the definition of a derivative since Pre-Calc. Of course, I still don't know exactly what to do when they only give you a graph that clearly isn't continuous and ask you to prove that it isn't using the definition, but I digress. Thanks a whole lot, this was very, very helpful.

[sillybillybg144]

you have no idea how much you help me

[RedTearS88]

i just love you .. thanks for explaining your the best ..

[ValleLucas]

Nice, not so professional but it's indubitable to say that it was well explained.

Normaly everyone uses the ''shortcuts'' without even knowing why it is that way, the best is to always understand how everything works, makes it easier to understand.

Hope eveyone goes well on their exams now.

[edwingindie]

would you marry me?

[ShaLuvLy]

I dont understand how you got t+h as a substitute

[Xoxocube]

Cheers bro.

[jbordon88]

Your videos are so very helpful! I appreciate them so much.

[JIKI900]

You are my HERO!!!

[RoxenMaiden]

*0*

I actually understooood!! =D thanks!!

haha!

[j20inch]

Im slow how did u get 4t^2+4t+4th+4h in step 4

[j20inch]

ok foil method....but the 4's?

[vallakan]

why can you make our lives easier than our professors?

[patrickJMT]

cause i care a bit more about teaching than do lots of them

[yaz90jordan]

because your the man :)

[tehs4ndman]

you did help me but i still feel confused lol