Basic Derivative Examples

[90blueg]

I'm taking AP Calculus AB and I am failing with a D. Anyone who understands calculus really well, willing to tutor me? I got a 5/50 today on my test :| Thanks

[zarp29]

Why is the derivative of a number 0?

[patrickJMT]

@zarp29 cause a constant does not change, hence its rate of change is zero

[Damnnnyoutryna]

lol youtube teaches me calc,programming,piano,cooking and gives me dating advice haha...literally the best site ever since there are people like you sharing your knowledge!

[Coolbluegirl77]

So awesome!!! And who would dislike this video? Gosh people

[magnusk750]

You literally saves my... I'm studying on a distance course in a foreign language, teacher extremely unpedagogical the few times we see her. Same thing every time, I understand absolutely nothing after lessons, then I go home and watch a few videos that a guy on the other side of the planet has made and share with us for free and slowly I begin to grasp. It'not easy, it's a slow process, grades not the best but I do push through somehow, thanks to you!

[actionjessie]

Patrick, you're starting too be sexier than Sal Khan x Thank you for making my engineer dreams come to fruition

[patrickJMT]

@actionjessie happy to help : ) especially since you have a joy division song on your profile

[awefilledcreep]

so im having trouble with the derivative of 6*x^(1/2) in the equation

5x^3 - 2/(x^2) + 6*x^(1/2) - 18

I got 15x^2 + 4x^-3 + 3x^(-1/2)

but then i looked up a derivative calculator and got 3/x^(1/2) which makes no sense to me after following the derivative rules.

help please and thank you

[patrickJMT]

@awefilledcreep how did you go from - 2/(x^2) to + 4x^-3?

[martin4o2009]

Great explanation, but i never understood what are d/dx

[jojogirl2008]

thanks so much!!

[XOpTicCyBorgX]

I love your videos man, fucking love them.

[glitters171717]

YOU SIR, ARE A LIFE SAVER

[socerplayer23]

While i was doing my homework on basic derivatives i thought i heard you say that 0 to the 0 power is undefined.

Is that a stupid question asking you that.

btw you are really good at explaining things.

If it wasnt for this video i would of gotten a F on my homework so.... Thx!

i understand how to do basic derivatives because of you :)

[socerplayer23]

why is 0 to the 0 power undefined?

[patrickJMT]

@socerplayer23 what should it be?

[socerplayer23]

@patrickJMT I was wondering because i thought it was 1

[patrickJMT]

@socerplayer23 why are you asking that question on this video though?

[AnotherBrownKid]

@socerplayer23 good question

[awefilledcreep]

@socerplayer23 dont mess with zero, it will haunt you forever >.>

[cherrypieee456]

This is a good video; i like how you thoroughly explained the process of finding derivatives. The only problem i have is when i couldnt see what you were explaining for #8 (because your arm was in the way)

[GreekBeast02]

Thanks for the video :D

[joesl8]

Isn't Pie raised to a 4th 4Pie raised to the 3rd?? I'm soo confuse???

[patrickJMT]

@joesl8 first, it is pi, not pie. and pi is a number, not a variable so the derivative of pi to any power is zero.

[joesl8]

@patrickJMT

Thanks for clearing this up! BTW I prefer pie to pi.

[patrickJMT]

@joesl8 i like them both!

[ZWATER1]

thanks bro for the info.peace and god bless.

[egancaubang]

Sometimes I wonder why did I even pay for my tuition fees,when i have you and youtube.

[xShiinigami]

OPTIMUS '

[lordthorpez]

as always... patrickJMT delivers

[ian559fresno]

WOW! 1084 Videos, Wonderful. Thanks for taking your time to post these. I don't care if they are taken with a flip phone..Its better than nothing...heck its better than most teachers.

[KoreaXFan]

You should remake the video with better quality :D. And on paper like your other videos. It makes it so much easier to understand and view.

[simsimaz2]

great job, keep it up

[WeekendWarrior1210]

Not a huge deal, but you've got two number 5's. Threw me off a little after writing down the problems. Great vids man, really.

[patrickJMT]

@WeekendWarrior1210 ya someone else pointed this out. i have a hard time counting past 5

[abuelT]

r u a professor or a TA?

[patrickJMT]

@abuelT who said i am either?

[JerryV06]

is V^1 the same as V? on problem #5

[alexhighflyer]

i'm left handed too :)

[stgc1993]

my new favorite channel

[Juriello]

When you said t squared you wrote t^1/2 on problem 6. o.o

[patrickJMT]

@Juriello my brain does not work so well

[Zilchary]

I passed math class thanks to this video!

[Sartaj94Nemesis]

Thanx buddy for putting up this video.. gr8 help! Cheers! :)

[Thrax005]

so what do derivatives represent in reality, what's there use in let's say physics?

[torres0efron]

I love your accent :3

[patrickJMT]

@torres0efron ha, kentucky boy accent.

[stupidintellect90]

Is derivative the same as differentiation? I live in England and I've noticed we use different terms.

[favz1]

even after watching this like 7 times... i still dont get it..

[MendoBud640]

great video, thanks for posting it, you are very kind and helping thousands.

[yskulkarni100]

Thanx 4 posting

[thew00ted]

u r incredible 4 posting this videos

[agleno]

great video thanks! you wrote 5) twice! there is 9 questions not 8! :-)

[imaniggforell]

you should skype me and help me learn this stuff. i'd payy youu. i bet you a lot of people wouldd...

[EngAbuFahd]

you really explained in a great way

thank you are my best mathematical teacher in YouTube

[TheDubCollector]

Im sure you've already noticed but Ill say it anyways, at around 4:56 you said "t squared" when it was supposed to be "t to the one-half", but you wrote it correctly.

Btw great vids, I made an A on my first test involving limits....you have really good ways of explaining

[patrickJMT]

@TheDubCollector ops, my mistake! i have a hard time writing and talking some times : )

[LuceroAnai]

all your videos are great

Thanks for taking some of your time in making these videos

they really help ;)

thank you!!!!!!!!!!!!!

[u2ubeac]

Thanks Patrick....you're doing a good job..I watch ur math tutorials when I do not get the concept at class and they help a lot. I wish I could contribute Elmo kind of projector the one other tutors use with web-cam, etc. Not sure the name of the projector they use.

[patrickJMT]

@u2ubeac this was one of the first videos i ever made, so it is not the best production quality : )

[serefliuser]

well done!

[gulamehussain]

the derivative of a number is zero its true but explain to beginers with defination of dervative as its rate of change in variable and where there is a number and no varibale there is not rate in varibale so total rate is zero

[patrickJMT]

@gulamehussain you can explain it. go make a video.

[masroor45]

thank u .........

[popedarren]

Really good job. I don't think you make things too complicated, but I do like to see what you're writing, so you might think about changing the angle of the camera, or stepping away from the board to explain with a laser pointer or something.

Thanks again!

[fonzi0was0cool]

sorry patrick, but your explanations are way too complicated. you need explain things in a laymans way, from the basics. as a lot of people that see your videos, including myself, are completely new to this...

[wojtek3016]

in the third example, root of 20= 20^1/2

therefore the derivative is as follows

1/2(20)^-1/2 = 10^-1/2

am I right?

[VVACID]

@wojtek3016 I'm pretty sure that there is a reason that the derivatives of all constants are 0. And another thing, you just stated that 20^1/2=10^1/2 Don't you mean root of 20=20^1/2=(1/2)(20^ -1/2)= (1/2) (1/{20^1/2})= 1/(2{20^1/2)= 1/(4{5^1/2})

[VVACID]

@VVACID oo, i just noticed what you meant. I think you just did multiplication before powers/indices.

[TheEirica]

how do you find the derivative of 1/ (sqroot x) ??

[TLucretiusCarus]

@TheEirica - The derivative of 1/x^n = -nx^(-1-n)

[ashleypina1]

@TheEirica This can be rewritten as 1/x to the 1/2. To get the power of 1/2 out of the denominator you will have to put it in the numerator while making 1/2 negative. So you will have x to the negative 1/2. Then you can use the derivative rules of multiply x by 1/2 and subtracting 1 from the exponent.

[odinheim]

that is easy to solve

[iceobreakers]

thank u!

[AMEchief172]

dude ur awsome!

[shadowlord5589]

check 5) and 5) looks like you made a mistake!

[cilicon]

Nope, he did it perfectly fine.

[GumFish]

Hint: Count the amount of problems on the board.

[cilicon]

I don't see any mistakes in 5) and 5). Both of them are derived perfectly with the exponent/chain rule.

[GumFish]

Yes. Yes they are. Very good.

[creativeartist07]

ur v looks like an s or kinda squareroot...hehe

nyc work..u helped me in my quiz..

[OliveOyl001]

thank you:)

[MrWyte1]

Amazing teaching skills! I am usually lost during class, but a few minutes watching your vids puts me right back on track.

[john650]

i love you man! will you marry me?

[antonjr]

How about d/dx(x) = ?

[beqfran]

d/dx(x) =x

[jhorv17]

d/dx(x)=1

[creativeartist07]

its 1

[jajaja295]

Can I hug you?

[TheMrHandyMan]

Hey nice video!

You should consider Livescribe Smart Pen or something though. If you're wondering what that looks like check out my videos.

Spread the knowledge friend!

[xxyxexmxi]

Very direct and pensive. Kudos!

[channokhang]

two question 5)  here

[codaro100]

thanks, this was very helpful. and im left-handed too by-the-way! just remember we are way smarter than right-handed people!

[upabittoolate]

Maybe but ambidextrous are the smartest (just the most uncoordinated).

[sazer123]

Could you imagine learning this stuffs(engineering math for me)..in a Problem-based-learning environment?it's difficult lol

[ExquisiteDoom]

I don't... get it. Is this derivative thing the same as algebra? It seems to have different rules , my algebra skills are a bit rusty but it seems to have some other law i don't quite get.. Any idea where i can have more info about this?

[iNick3]

Derivatives are part of calculus, which is basically more advanced algebra. I haven't taken calculus yet (although I will be taking it this year), but I believe the derivative of a function shows you how the graph of that function changes.

[ExquisiteDoom]

oh shit, that makes sense now. Short, but right to the point, and clear. Thanks alot mate, now i can start making sense of all this.:)

[boorens18]

the derivative is used to find the slope at a point on a curved line

[SaintsRow2fanatic]

its the GRADIENT function, of the function. If you get a derivative of a function, u get its gradient function, simply by substuting an x value will give you the gradient at that point.

[zantrua]

look up the definition of a derivative, it should help :)

[ThomasNFLD]

... calculus... uses algebra but is not algebra. it's calculus...

[napalm4sd]

This is Calculus, quite different then what your use to in algebra. Though advanced algebraic techniques are needed to solve many Calculus problems. For example, before you learn this method for solving derivatives, you would actually solve a derivative using something similar to the "difference quotient," you learned in algebra. This method is using the Calculus method, and is much easier.

[armeijamies]

thanks for the help... I did notice number 4 you forgot the neg sign when you brought down the exponent

[sobeita]

X^-1 = 1/x

X^1/2 = sqrt(x)

Square root is one-half power, nothing negative there.

[schlynn]

1/2-1=-1/2.

[sobeita]

Ah, I see what you meant now. You're right.

[localbroadcast]

hard to read.

[nibauAntunes]

yes, that's it!

[Denis150386]

So where the derivatives can be practically used for? :) Can you tell me some examples..?

[nibauAntunes]

in physics, the acceleration is the derivate of the "speed function", for example.

good work patrick

[patrickJMT]

technically, i think it is the derivative of the velocity function : )

[fingerboy18]

@nibauAntunes Position, P'=Velocity, V'=Acceleration, A'=Jerk

[nibauAntunes]

@fingerboy18 before insulting somebody you should think first. my native language is not English, so i mistranslated velocity with speed! you didn't teach me anything, jerk!

[fingerboy18]

@nibauAntunes I wasn't insulting you, I was putting the comment for anyone that didn't know.

[nibauAntunes]

@fingerboy18 ah lol then i'm really sorry. i though the "A" was from "Antunes" lolol Ok, yes, you're right, (Acceleration)'=Jerk. yeah! sorry man! really!!!!

[fingerboy18]

@nibauAntunes :) it's okay haha!

[damnaladen]

wow...IT MAKE SOME SENSE..

[chubble101]

thanks alot for he vids man.. really appreciate it!

[imrama]

Thanks Dude.

[Desrathedemon]

d/dx(10v)^2=100

d/dx((10v)^2)=200v

[guchaman]

either u did number 10 wrong or u did number 2 wrong. check that out

[MetallicaFTW7]

uh im pretty sure there's only 8 problems... lol

[6635060]

i like to be involved with math caz i love it much much

[revolutiongames2004]

i thought 0^0 was 1..

[patrickJMT]

0 is a real number

[panefuldeath]

0 is a real number, and 0^0 is 1...

[panefuldeath]

no i lied, 0 is a real number but 0^0 is infinity.

[InfiNiteXeno]

That's not right, 0^0 is undefined, yes it is infinity but how large is infinity? Same thing as x / 0 = Undefined "Infinity"

Otherwise, good vid, but do give us some more advanced tuts

[damnaladen]

yes..it's undefined..any number divided by zero is UNDEFINED!

[bee3108]

thanks a lot,i can study at home by this way.comfortable and easy-understanding;-)

Good job

[gtech90]

MyWheysTheWay, it's a small mistake - get over it. You should be praising the man for his effort to fork out these videos for calculus students rather than insulting him.

[olsome2]

why would d/dx (10v)^2 be 200v and not 20v

[happydude8815]

because u have to use chain rule so it would be

2(10v)(10)=200v

[happydude8815]

or even (10v)^2=(10)^2 v^2 =100v^2=200v

either way is fine

[SFaily]

don´t forget about the inner derivate

[MyWheysTheWay]

theres 2 number fives...ironic... because hes teaching math; yet cant count ?

[aggiefitz]

My algebra is pretty weak, so how would I take the derivative of f(x)= (2x^2 +2x+)(e^x)

[sakuranohana89]

consider 2x^2+2x as a function that you can call f, so f=2x^2+2x , and another function that you call g, where g=e^x.

the derivative of f*g= (d/dx*f)*g+ f * (d/dx)*g

so your derivative would look like this :

(2x^2+2X)(e^x) = (2*2x+2)*e^x+(2x^2+2x)e^x ( the derivative of e^x is e^x)

so you get e^x ( 2x^2+6x+2)

I hope that was clear enough, I'm not a native English speaker, but I tried to explain it as easily as possible :)

[aggiefitz]

Clear enough. Thank you.

I hate this crap, I am much better with chemistry, biological sciences. I don't need to know the derivative of f(x) when my patients heart stops :)

[fingerboy18]

@aggiefitz No one really does, math is just a way of developing your skills to think a specific way. Although, some people do need it like us Engineers.

[Rivcor]

Derivative of square 20 is not 0....

[xb0xher0]

what is it?

[Rivcor]

square of 20 is the same as

20 to the power of 1/2 and then u use the power rule

[WrathofTulkas]

(20) ^.5 is a constant... the derivative of a constant is zero...

[MJA0869]

I wish YouTube was around in the late 80s when I took Calc...I would have done a lot better!

[Mediterraneanblue9]

Ya, but all this technology has us current students lazy, dependent on technology, and less creative.

[mareey]

your voice is so friendly which makes it that much more effective!

[patrickJMT]

and yet, i am such a mean guy in real life!

[dorothydorothy111]

Hey patrick, the 'basic derivative formulas' video isn't on utube...i found it on your website..and it is from google video..just thought you might want to know there wasn't a link ;-)

[patrickJMT]

yep, not all of my videos are on Youtube... i originally posted them to google video instead, and some of them are still there.

so.... the complete list is regularly updated on my website!

[dorothydorothy111]

cool...i am sooo glad i found you...i would be so lost if not.

[patrickJMT]

now, all you need do is reach into the aether that is the internets... i will show you the way

[dorothydorothy111]

lol

[omairgeforce]

i cant understand 5th

[fredarc]

Hello! Yeah I have just been looking for some basic vids about this level of math and I find these really helpful.

Looking forward to watch all of your tutorials, and hopefully one day I will be able to repay the kindness of all guys that make self tutoring and education possible and even fun! tHanK YOu!

[keiraiarm]

nice job.you made it simple and easier to understand.better than our professor..

[RainArgifel]

ty...it really helps me a lot

[therotaryrocket]

This is the first video in my evening of searching calculus videos that gets basic enough for me to understand without watching it twenty times. I'm taking Cal 1 and have not taken the right prerequisite so this is definitely helpful. I'm subscribing, thanks for putting this and all the other info out there!

[patrickJMT]

no problem, good luck in your class!

(i have vids for a lot of calc 1 and calc 2 stuff that is better organized on my website!)

[hannahlouiselogan]

How is it that you're so good at maths but labeled your question numbers as 1,2,3,4,5,5,6,7,8 haha

[patrickJMT]

ops! : )

it is to make sure you are paying attention!!

[hannahlouiselogan]

Thanks you've basicly saved my a-level core mathematics!

[yasir25119918]

plz help upload a VID of Interegation or Anti-Derivative .

[patrickJMT]

uh, i already have about 30 of them... look a little harder : )

[saifeestar]

strong base mains strong structure .... good job.

[patrickJMT]

thanks!

[system0system]

Great Stuff!!

[patrickJMT]

thanks friend!

[najjar89]

thanks patrick, my calculus teacher sucks but your vids helped me understand better

[atomo360]

thanks alot