Related Rates #1 Problem Using Implicit Differentiation

[BlastedCrayonx]

I just might not want to do awful things to myself during AP Calculus anymore!

:D

[woofmeow93]

What book are you using? Just curious:)

[gabnadal]

DREDS

[theACE4554]

i love you

[JH5251]

Thank you so much Patrick!

[kighler36]

i stopped going to lecture when i realized i can just watch these videos in bed.

[DaDude458]

I love you patrickJMT!

[lyckitysplyt10]

you've seriously helped me through this semester. thank you

[HatDamage]

Disregard Calc Lectures

Watch patrickJMT

[msdwizzle55]

thank you so much. I have a test tomorrow on implicit differentiation and related rates. this helped me out so much.

[OhHiMeMatt]

if only you taught every subject, my GPA would be a 4.0

[mage1413]

holy crap Patrick, no matter what year of math I have taken, you always made videos on every section in my textbook. I am in first year uni now, and we're doing related rates, so this video was very helpful. Also when I was grade 10, I remember you doing a "completing the square" video which helped me out a ton. you are great

[Jb4031]

you have the same math book as me... do you like this book out of all the single variable calc books?

[009ChipsAhoy]

do you have the Single Variable Calculus book by James Stewart, if so i have the same book!!! (i noticed due to the baseball diamond picture at about 0:28)

[zero6140]

is their others way's to support you like clickling ads or something..i dont have online money

[patrickJMT]

@zero6140 i am not allowed to encourage people to click the ads in my videos ; )

[pigsbum53]

all hail the math king

[patrickJMT]

@pigsbum53 : ) 

[hahatrolledbabe]

isn't x=150? Because 35(4)=150

[patrickJMT]

@hahatrolledbabe i think your math is a bit off

[Machammerballs]

@patrickJMT I love your responses almost as much as I love your videos, they're always so polite they just make me smile!

[ian559fresno]

@Machammerballs I know, its hard to deal with trolls sometimes yet Patrick still manages to.

[patrickJMT]

@Machammerballs ha, often i am not so nice : )

[ryandanroth]

@hahatrolledbabe I think he missed your name in the comment.

[DragonRider520]

@hahatrolledbabe Well... if u cant do that in you head, i think it would be quicker if you just grab a calculator before asking a question like this.

[Kryptoslol]

Did you by any chance do problem 19?

[ctnaa]

thankyou!!

[quantumhm96]

thats my calculus book!

[mrwooknguyen]

this video is godly

[KatieS618]

oh and im talking about 7edition book

[KatieS618]

Can you tell me why the back of the book for 2.7 number 19 says the answer is 720/13~~55.4km/hr maybe im missing something really simple..?

[hersheybar310]

qhy do you make these videos? what do you get?



[patrickJMT]

@hersheybar310 i do not speak internet speak. i have no idea what qhy means.

[Kcvee777]

@patrickJMT he meant "why" llol  presseed Q

[patrickJMT]

@Kcvee777 ha, ok

[cdilJ]

@hersheybar310 ....Respect

[SarahIsShameless]

i still dont freaking understand these! i hate calculus. time to watch more of yer videos to see if i can get these.

[durrthock]

My teacher thought us this Monday, and put it on an exam Thursday.

[patrickJMT]

@durrthock so?

[durrthock]

@patrickJMT No time to study it, had a full week of other classes.

[patrickJMT]

@durrthock that excuse does not work on me. i took 18 credit hours in college while working 40 hours a week and still found time to study the stuff i needed to study. better to say: it was not that important to me.

[bjjc51192]

This is a bastard of a change of rate problem.

[ogmasterkiller]

Is That a stewarts single variable calculus 7e textbook

[jcklw1]

get a better mic. good vid tho

[patrickJMT]

@jcklw1 make a $500 donation and i will go pick one up tomorrow.

[DJSt3v3n]

wow, if only there were a video for every single math problem I didn't understand =D

[pvbchic]

Wait, so what's the answer?

[TrAnScEnD3nT]

can you teach teachers how to teach? thank you.

[patrickJMT]

@TrAnScEnD3nT ha : )

[houghtboysftw]

Derivative of a constant is 0. Derivative a variable is 1, unless it is in respect to something. In respect to x, the derivative of x = dx/dx, so we just say one. However, the derivativeof y = dy/dx.

[FatalP3rfection]

I wish I could do Calculus with a Sharpie...

[imwithdumbhead]

3:19 "i'm gonna leave my units out cuz im lazy" i thot im the only one here. haha

[kellyh38]

I have the same calculus book!(: I've watched your videos since last year, you're awesome! You probably get that a lot but honestly, THANKS!

[seifdeiab]

isn't the derivative of 100^2= 200^1?

[patrickJMT]

@seifdeiab no. it is zero. what is the derivative of 10,000?

[seifdeiab]

@patrickJMT oh right.... thanks

[JasonKwon69]

Thank you so much!!! I will DREDS until I die!

[scorpion22008]

@patrickJMT no doubt that lefties are mad smart :)

[Salamero500]

awesome video thanks for breaking it down.

[07minute]

heheh, shameless plug =] love it

[bmcbls]

"I'm gonna leave my units off cause i'm lazy." It's glad to know we have something in common...

[LinWilliam]

college professors... y u make calculus so complicated!!!

[potentialavalanche]

Because this is marginally more convenient to read:

At noon ship A is 100 km west of Ship B. Ship A is sailing south at 35 km/hr and Ship B is sailing north at 25 km/hr. How fast is the distance between the ships changing at 4 pm?

[DroGolfBulb]

can you solve related rates without using implicit differentiation? as the title suggests?

[light832]

Yay lefty!

[CaNaDiiAnBaCoN]

I have watched so many of your videos and i just thought of something. where is your camera?

[OZZl3]

This video was extremely helpful thank you! However I find it easier to understand if you write it like this instead:

z(t)^2 = 100^2 + (x(t) + y(t)^2

Dt( z(t)^2 ) = Dt( 100^2 + (x(t) + y(t))^2)

(Using Chain rule, look up if you don't know it) =>

2*z(t) * z'(t) = 2(x(t) + y(t)) * (x'(t) + y'(t))

Then you just juggle it around with some algebra to solve z'(t). It looks neat I think and it's easy to keep track of what the diffrent variables represent, x'(t) is the change eg km/h and x(t) etc

[cappuccinolalala]

omg~ u stopped at the hardest part

[OZZl3]

@cappuccinolalala if entering the numbers into the calculator is the hardest part for you then maybe you don't need to watch this? :p

[kwarkn]

Wouldn't there be a negative for the ship moving south (or vice versa) and for the ship moving north? Im asking this question as in signs (- and +).

Thanks.

[patrickJMT]

@kwarkn no. you should not think about positive and negative as on an x-y plane. if the lengths are increasing as time progresses, the derivative with respect to time should be positive (to indicate it is increasing)

[FutureXGeneration]

"I'm too lazy to write it out.."

YOU DICK :P

HAHAHAHA

[danielleychick]

i love you btw lol

[vbhatt24]

Suppose, ship A was going east instead of south.

Would that just make the pythagorean equation become:

(100 + x) ^2 + y^2 = z ^2?

Thanks.

[brettbed]

This is from the Stewart Calculus Early Transcendentals. Great b

ook for learning Calculus. Wish more teachers used it.

[Thejugglingbum]

OMG this is crazy! I take on online calc course and the practice problems and the tutorial aren't working but this is the EXACT problem I needed help on.

[patrickJMT]

@Thejugglingbum send your payments to me from now on.

[drbenani]

you are so helpful omg

[Mydrall]

I love your tutoring. It is the only thing keeping in in class. Without your videos....I am afraid I would be totally lost. My own teacher is terrible. Thank you.

[HeroOfXanadus]

wtf was my professor talking about for an hour and a half?

[bossbower]

Just what I needed! Thank you!

[poopawman]

oh my god

you're using the book i'm using for calc class

[Mike01010011]

Thank you so much. I have been struggling to understand related rates and this video really helped me understand! Thank you so much!

[ephue]

omg this is my calc book! we did this problem in class and i didnt understand it. let me watch the vid and see if i do!

[Ameliajandreski]

Why didn't you use the equation 2A da/dt + 2B db/dt = 2c dc/dt once you had your right triangle ?

[hi123people]

DT=dark templars

[HokiefanStarcraft]

@hi123people Dude whenever my teacher says "DT" in class I instantly think that and get distracted!

[lifemakesmelaf]

ive watched a lot of your videos but it didnt hit me that jmt stands for just math tutoring until just now :) and ive seen that little "shameless plug" more than a few times now haha

[dldnch]

umm.... im just plane stupid so i don't get it 100%, although you are obviously a really skilled teacher... why is the dx/dt required when doing the implicit diff.? because x and y are both in the y direction?

[Isk8emericas]

dreds that definitely helped man thanks

[Hoz2001]

HOLY SHIT!!! The problem you did was the exact same problem I needed help with!

[KASAfreakinBLONKA]

Why can't teachers teach like you!?!? It's their freaking job, the one thing they have to do, and they are completely incompetentX( I. love. you. You just saved me from failure.

[d3mur3]

thank God you exist! 

[paulojunior201]

these ads are so annoying

[ducktapexartist]

I have a HUGE calc test tomorrow, and I couldn't be more confident after watching this video. Thank you so much!!!!

[vplof]

Thank you, my teachers cant explain it 

[mortsdans]

8 teachers watched your video and were jealous

[patrickJMT]

@mortsdans ha

[hopeira4622]

@mortsdans its 9 teachers now ;D

[EGOsoBIG94]

my teacher uses this book...we gotta test monday, i hope you've done the problems he got from it. 

[skatingisphun]

OMG patrick, you are a god. I have a quiz on related rates tomorrow and had no idea how to do these problems until I watched this video!!! thanks!

[FrankBooth99]

"and now dear viewer..."

classiest way to break the fourth wall!

[ronmascara]

@FrankBooth99 hahaha so true 

[thewingedone162]

you did an amazing job breaking this down

[petermilko]

MOM! stop vacuuming!

[patrickJMT]

@petermilko it was probably the yard guy, cause my wife and i both hate vacuuming!

[n8ivebl00d]

Awesome videos. It's a nice review for my test coming up.

[gouki02]

mmm the physic part needs to be explain, you know what im talking about! like distant´s derivative is velocity kind of shit

[jnmrcbrown1]

You sir are like Moses ushering us in to the promise land of understandable Calculus!!!

[mrsogata]

@jnmrcbrown1 HAHAHAHHAHAHAHAHAHA

right on buddy!

[romyboy]

tnx to your videos i really improve a lot in my related rates problem by watching your video you added another in my tool kit tnx

[webmastertool]

Calculus Early Transcendentals - I love that textbook, it's the one your using.

[llcooldre75]

Is that Stewarts Calculus Textbook??

[patrickJMT]

@llcooldre75 maybe!

[psalm10433]

@llcooldre75 the real question is what version lol

[esmartemars]

@llcooldre75 yes! 5th edition I got the book

[MrRingTingTing]

Patrick, you are saving my life for my AP Calc BC final. Your videos are great and infinitely helpful - what you do is important and very, very much appreciated. Keep up the great work, and thank you so much.

[wenya87052]

You saved my life. Ur teaching skill is way better than my calculus teacher. I finally know what's going on. Thanks s lot

[jeroen360]

lol im 17 and i understand this :D

[patrickJMT]

@rob5654 i independently created calculus while in the womb

[Alexsy82]

@patrickJMT i invented the concept of zero as a fetus.

[YukonTrooper]

@rob5654 Let us know when someone cares.

[onyxfig]

@rob5654 I understood this when I was 13 and I started multivariable calculus when I was 16, stop bragging

[mypinkdollprincess]

DREDS is an effective way to solve this stuff. Thanks Mrs.PatrickJMT!!

P.S. Please convey my "Thanks" to her(:-

[Sectorsophia]

I don't even WANT to know how to do this! Grrrr lol.

[patrickJMT]

@Sectorsophia so don't learn it

[JayZeus7]

You inspire me to get a secondary in teaching.

[sclub7stargirl]

You did a great job explaining; I understand it. Thank you.

[glenntadams]

Couldn't the implicit differentiation be sidestepped instead by imagining one ship being held constant while the other instead moves 60 km/hr (35 + 25)? It's all relative motion anyways. I got the same answer. Is this a fluke or am I on to something?

[bchiz6]

this exact problem was on my midterm.. I wish i seen this before i wrote it. maybe i would not have failed :(

[horrabletypoe]

As much as I appreciate my professor's constant puns (sin(x) is good for hayfever), you have probably been the biggest help to my progress in my current maths courses. So, thankyou :D

[sweetpeapinkadot]

could you still find it if you kept it in 2 triangles?

[nuvydeep]

i just have a problem coming up with the geometry part for the diagram.. :( But good video! Thank u

[NeoXC]

Sweet! I finally got one right! These related rates problems seemed very difficult at first, but after cramming and practicing for a while, I did your problem before I watched your video and managed to correctly do it. :) Great video!

[patchesohola]

amazing. fuck teachers we need more youtube fuck foreigners

[Nile505]

I have been watching my teacher do these for 2 classes now...and you actually showed problem solving steps..I hate my professor. She just implies that we know EVERYTHING up to this point. She never recalls anything for us, and she just skips over steps. Thanks for the vids man

[ojoreakatheoj]

Ah this makes review so easy. I took calculus about 4 years ago XD.

[rockerforlyf]

thanks for the DREDS mnemonic!

[patrickJMT]

techincally, you will have to thank my wife - she told it to me!

[sanjor8r]

@patrickJMT do you have a mnemonic for optimization problems?

[Telepcanin]

Would the rate of change be the same at 3 pm as at 4 pm ? thx for video !!!

[username14657]

You really strip down math to the problem solving adventure it should be. Everything is less intimidating when explained in real-world terms. Thanks!

[cccspwn]

kool I use that book !

[hockeymo]

shoudnt 35 be negative?

[patrickJMT]

no. both distances get longer with respect to time, so they should both be positive

[NeoXC]

@hockeymo No, it isn't negative. If it was negative, ship A would actually be moving backwards (north) toward ship B.

[andy120692]

DREDS, won't be forgetting that.. Good problem choice for a video.. took a lot of substitution and thinking to come to your answer

[BrendaGoes123]

ohhh wow. so much work

[irreverentmoose]

Can you treat both the x and y movement as 1 variable?

[179600]

Yes! I have the same book!!!!

[chattersworld]

I GOT THE SAME BOOK! YAY! I LOVE U MAN

[qwertyaznman123]

You know, you probably shouldn't have said "the change in the x direction" because it doesn't make sense on a set of axes. Technically dx/dt and dy/dt would both be on the y axis. It just sounds confusing when normally x and y are on perpendicular axes (like on a graph)

[AureolaFE]

In this problem, though, X and Y aren't referring to the axes, though, there simply opposite directions.

[qwertyaznman123]

Yes, I understand that they were opposite directions, but I was merely commenting on how it might be confusing to a viewer that usually denotes x and y to perpendicular axes, and might instead use a and b rather than x and y to denote that sort of thing.

[AureolaFE]

Yeah, you're probably right.

[saturnv3]

Awesome! Much better than my teacher...

[NicholasAABBoy]

this problem is similar to the one i have in the Cal book..but thank you for helping me understand more about this type of problem...

[Liist]

Awesome, I use the book.

[21ttliyusu]

thank you so much, you are a lifesaver for my calc. test tom, i'm swinging by a donation :)

[tkeo]

Thanks! Helped me a bunch, and you explained it very clearly.

[mparfait3]

Thank you for posting this video it really helped me out :) !!!

[3x10tothe8th]

Thanks for posting! I thought that I had understood this concept in class, but I guess I forgot it between then and the time I started my homework, so seeing this done again helped A LOT! Thanks again! :D

[kzak911]

Thanks man, really apperciate it!!

[xxelyanaxx]

In the 6th edition book they changed the problem from 100km to 150 km. Just pointing that out in case anyone is using the 6th edition and not the 5th. It's problem 14 in section 3.8.

[Tuufless]

Another method which may be worth mentioning (that doesn't use implicit differentiation) is to note that the height of your right triangle, x+y, increases at 60km/h, or can be expressed as just 60t.

Using Pythagoras the same way, you get

z = [ (100)^2 + (60t)^2 ] ^0.5

Differentiate with respect to t, substitute t=4, and you're done!

This method should be easier, since you had to use some form of z(t) in the end anyway. I suspect you were forced to diff. implicitly. :)

Good job on the video!

[greatmoose]

u are a fucking machine!!! wish my teacher would never make mistakes or trail off and talk about his personal life........... anyway ty sir

[patrickJMT]

glad you like them... but everyone makes mistakes, me for sure!

however, i can either delete the video or at least make annotations if it is a 'small' mistake! : )

[ephue]

@greatmoose real talk!

[kashiark]

i dont understand how you know which one to put on top i.e. dy/dt you said with respect to time but i dont understand O.o

[tony225]

The way I think of this is that "with respect to" means something like "in terms of" and that part always is on the bottom.

So it would be dy/dt and dx/dt because the function that I am looking at gives me some value (for x or y) depending on time (i.e. it's based on whatever the time is at that point. That is, tell me some value for t and I can give you an x and a y value at that point). That's how I think of it anyway.

[djm003]

Ok im in the library at OSU and not only did this help immensely but it was word for word the problem that I was working on in my book. Great explanation. Thanks a lot!