Related Rates #2 Using Cones

[Sadena123]

Great videos! Are you a student yourself?

[patrickJMT]

@Sadena123 not any more! but aren't we all students of life? : )

[KFUPMs2010]

why you don't film this with more quality it seems old (1990) take a nice camera and continue >>> however ,thank you very match

[patrickJMT]

@KFUPMs2010 that is cause i was using a crappy camera at the time. deal with it!

[pearlwhite21]

why do u keep pi/12 when u get the derivative? why doesn't it turn to 0?

[TheBlazeofRazgriz]

@pearlwhite21 the pi/12 came from the derivative of 1/3pi(h/2)^2

[pearlwhite21]

@TheBlazeofRazgriz thx :)

[BeastlySin]

@pearlwhite21 because pi/12 is a coefficient and not a constant standing alone. it is like if you are taking the derivative of 2x^2 you get 4x. so in essence the pi/12 and the 2 are the same thing.

[pearlwhite21]

@BeastlySin ty :)

[crossforced]

i fucking love you

[marioman619]

Thank you! It helps that your handwriting is really neat. Every time my classmates point to their work and explain, I don't see what's going on. Really, thanks. It's MUCH easier than I thought.

[Raffee010]

why is this so easy when you do this? :P Keep up the great vids!

[RhaynnxLoveMusic]

DANNG my teacher used this exact question in our quiz!!

[patrickJMT]

@RhaynnxLoveMusic hope you got it correct :)

[beaver2264]

Hey Im a bit lost on where the dh/dt got there, why would you multiply it by dh/dt

[patrickJMT]

@beaver2264 implicit differentiation 

[sammyhtb]

thanks for helping me graduate high school and helping me in college right now!

[sammyhtb]

love ur vids. please do a vid on related rates with cylinders! thx

[ribbonwing]

How does that dh/dt get in there at 1:47? Shouldn't it be dh/dv or something?

[patrickJMT]

@ribbonwing you are taking the derivative with respect to time, hence the dt

[orangegold1]

@ribbonwing It didn't make sense to me either, and hit explanation doesn't help at all... now I see it though... on both sides of the equation the 1/dt cancels out so you are left with dv = function * dh... that function is the derivative of volume... so it now says dv = dv*dh... dv candles and you are left with the solution for dh = 1, wait never mind.. I just confused myself.. I don't know what he is doing...

[orangegold1]

@ribbonwing Oh it came from the chain rule.. when he took the derivative it isn't just an exponent shortcut rule... It's chain rule.. you have to multiply but he exponent and the derivative of the function, then the original function, then drop 1 from the power. dh/dt is the derivative of said function.

[TheCombineAssassin]

How did you get h^3?

[redrum41987]

@TheCombineAssassin he put r=h/2 and its squared in the problem. so it would be h^2 over 4 then he moved the 1/4 and times it by pi/3 so it would be pi/(3x4) h^2 x h or pi/12 h^3

[SuperXD25]

the awkward moment when an advert is longer than the actual video..

[deis7]

Shouldn't your answer be in cubic ft per min

[patrickJMT]

@deis7 no, height is not measured in cubic feet. i am not 6 cubic feet tall.

[hahalala60]

why do you still have the pi/12 when you take the derivative on both sides? Isn't it just zero and shouldnt be in the last equation??

[cdilJ]

@hahalala60 ......when you take the derivative of "constant times the function", then the constant comes in the front. Basically d/dx ( c f(x) ) = c d/dx (f(X))....I hope it helps

[redrum41987]

@hahalala60 pi/12 is a constant multiple not a constant being added to anything. like the deriv of 3x is 3. only when its 3x +3 its 3+0.

[NLx360]

why do you leave the pi/12 alone in the beginning. It's just a number right? so wouldn't the derivative be zero?

[silverflame92]

@NLx360 no...there is an h with it....like the derivative of 2h is 2...!

[pvbchic]

@conman2317 How are you even in calculus... *practiced...

[LeroyTrey]

Why do we leave the pi/12 alone?

[AceAites]

@LeroyTrey You leave pi/12 alone because it is a constant. Remember if g(x) = k times f(x), then g'(x) = k times f'(x). This was the property he used.

[pennjersey83]

This is so hard

[applessuace]

Every example I find online says something along the lines of "height is always 1/2 radius" or "height and radius are equal." What if I am NOT given this relationship in my problem?

[Prickle]

sorry, dumb question, but how did you come with (h/2)? is that from geometrically because I totally forgot >.<

[captcalvin]

@Prickle h is also equal to the diameter and radius is simply half of the diameter, or h/2.

[flyingbeagles]

OMG HOW COME UR SOLUTION MAKES SENSE AND THE PROF DOES NOT

[flyingbeagles]

OMG I FOUND THE Q MY PROF RIPPED HIS QUESTION FROM

[buhoman3]

never mind.... im an idiot

[buhoman3]

why didn't you multiply pi/12 by 3 when u differentiated?( i dont hav sound on my computer)

[WingedAngel9]

i love you.

[DAsahutube]

This video was great! One thing that I think is an easy throw off it the height divided by 2. Since the height and diameter are equal than the h/2 and radius are equal too. Just to clear things up.

[espio142]

@DAsahutube Thank you!! I was wondering why he use h/2!!

[abney317]

squeared

[stsrawmos]

I would hate to do math or write even left handed.

[ouran909]

wow thank you for this! Definitely feeling better about rates.

[bulizazul]

lol thats quest from UTEXAS. omg hahaha i have that type of homework.

[Theeriuth]

you are awesome

[TryandbeClever]

where did h/2 come from?

[SolarFlare67]

@TryandbeClever The radius (r) is half of the diameter (h in this case), so plug in h/2 for r.

[chris082681]

@SolarFlare67 Thanks!! I HATE FINALS!! kill me.

[abney317]

@TryandbeClever

it's the radius

r = diameter/2

[bobsagetville]

i wonder if my teacher will know if i just use this for my project XD

[junior10tu10papa]

why is "h divided by 2'?

[Ricenugget]

@junior10tu10papa H is the diameter and you want the radius value, which is the diameter (h) divided by 2.

[FlufeehDarius]

Is that UTEXAS?

Oh god. >.<

[patrickJMT]

@FlufeehDarius u know it is

[H311archer]

I have the highest grade in my calculus class due to your videos. Thanks

[livvvylion]

you are so awesome. and really attractive :D

[dbpanther94]

can you calculate the rate of increase of my Calc grade as the # of your vids I watch increases?

[patrickJMT]

@dbpanther94 i would need more data first : ) which i would love to have actually; i would love to test a group of students who did watch regularly vs those who did not

[gvstatgal]

@patrickJMT I am a stats major if you need help with that at all =)

[alreadytakenthe3rd]

@patrickJMT They would have to all be taught the same way by their normal teacher for the results to be accurate.

[nnomak21]

@dbpanther94 HAHAHAHAHAHHAHAHAHAHAHAHAHAHAH­........................thats verrrryyy funny dude!!!

[MrHav1k]

@dbpanther94

lmao! great idea!

[MrKevinJiang]

Interesting. (20/(pi/12*3*100)) The reason why people are getting 4pi/5 instead of .254648... is strange. Punch it in the calculator you get the latter. Do it by hand and you get (1/15) times (12/pi) to get 12/15pi, simply it to 4/5pi, which is a different value. I'm rather confused myself.

[MrKevinJiang]

@MrKevinJiang Nevermind, now I know why people were confused. You need to put parenthesis around 5pi when you divide it, other wise the calculator wil think the value is 4/pi times 5.

[spliler]

Oh hey, I got to UT and I have a calculus final tomorrow, so thank you for this. Related rates seems to be my only sticky spot for some reason... Watching the rest of your videos for the remainder of my all nighter.

[dia8449]

thank god for u patrickjmt

[panchosan123]

isn't the derivative of pi/12 0?? or is there something i don't know??

[meganhewitt92]

THANK YOU!

[JorgePrima]

I think you miscalculated at 1:28 h^3 should be over 12. Or am i missing something? :(

[ownedncut]

I want to do sex with you. patrickjmt

[ZX9Rish]

why do i keep getting 4/5 pi

[Itotallycantfindname]

@ZX9Rish I do too, maybe there's a mistake?

[BIGBobJohn23]

more related rates problems plz :]...im struggling :[

[VersatilityInfinite]

hey, i'm working a similar problem but i have a hard time understanding it, it asks:

"The radius of a right circular cone of fixed h=20 cm is increasing at a rate of 2 cm/s. How fast is the volume increasing when r=10?"

so the givens are r' =2 cm/s or h' = 2cm/s? i guess in this problem the cone is upside down and as the h increases the radius is also increasing. Do you find V' wrt to h=20 cm first than plugin the r after you've found V'?

[1matth3w1]

hey patrick, at 1:53 is it ok to reduce like terms  when taking the derivative? is it possible to reduce the pi/12 and 3h^2 to pi/4 h^2?

[keithdk123]

@1matth3w1 I'm not Patrick, but the answer to your question is yes.

[IslamPlanet]

Your channel is the best I have ever seen on youtube as far as teaching math. Lots of helpful videos on complex and fairly simple problems. Most channels here focus on extreme basic math which no one needs really.

Are you going to explain advanced concepts in calculus like dual and triple integrals and or multi-variable calculus and so on by any chance?

Thanks a bunch!

[patrickJMT]

@IslamPlanet glad u like the vids. i already have quite a bit of multivariable stuff, including multiple integrals.

[sexycooljulesverne]

why not in fractions? decimals are for amateurs.

[Gotenks211]

why is the pi always left alone ?

[patrickJMT]

@Gotenks211 no one is hungry

[ksingler22]

@patrickJMT this was a wonderful comment. i thumbed it down by accident. i meant to thumb it up. by the way, its 3:30 in the morning and i have a calc test in the morning and when i'm looking up a calc topic on youtube, i specifically look for your name because you are BY FAR the best teacher on here. these videos are so appreciated. thank you, sir.

[patrickJMT]

@ksingler22 you are very welcome. good luck on the test!

[china2207]

@patrickJMT lol

[xlipsxdeceitx]

@Gotenks211 pi is a constant, not a variable. when taking derivatives, you leave the constant alone.

[RockSmithStudio]

@Gotenks211 because pi is a constant so it is not changed by the derivative.

[who8mahbacon]

@Gotenks211 because pi is just a number

[padard]

what if the radius is given in the problem, do you just plug it in or do have to find the radius in terms of "h"?

[dragonmasta91]

related rates and optimization are two of the most hated topics of mine in calc lol

[like9orphanz]

why do you leave the pi/12 alone at 1:44?

[Tyrantofthewind]

@like9orphanz

[Tyrantofthewind]

@like9orphanz

It is a constant.

[djlucario99]

YES!! thank you :D

[CameronK]

Many thanks

[yaynikki]

1/3 pi is a constant. so you just keep it

[theguyuknow1]

i just noticed we're both lefties!

[karlkarlkarl1234]

lefties are genetically deformed.

[jay16021]

thanks soooo much!!!!

[wtakphysics]

we are doing problems like this one consistently in my high school non ap calculus class

[nsupe]

Thanks man.

[yogesh892]

thanks so much this helped me with a problem i was stuck on for ever!

[mobilemagnolia]

when you took the derivative, is it the chain rule and the other stuff disappears because it's zero times h cubed?

[68hinduhammers]

thank keep doing what you are doing.

[marcusjhung]

the hard ones are the ones where you have to combine relationships and whatnot.

[kaileecripson]

ohmyloard thank you so much, I was about ready to cry I was so confused x.x

[robman17]

roughly .254648 only? you couldn't have been more precise? =D

[conman2317]

why don't people ever post the hard ones, I understand these ones, but the teacher will always put a tricky one on the test, that I've never seen before nor practised with. The teachers love screwing you over I guess. Teach you all the easy ones, then expect you to do a hard one like its a piece of cake.

[patrickJMT]

yep, teachers just love screwing over the students. it is why they become teachers

[WhatsY0UTUB3]

Lmao, owned.

[strat0caster266]

@patrickJMT

I sense sarcasm.

[tony225]

If you're using Stewart's book, or any book, really, just do every odd numbered problem at the end of each section. Or at least take a look at them. Hopefully you invested in the solutions manual (best investment I ever made in non-required material).

If you see a problem on a test that is unlike anything you saw in Stewart's, I would be really surprised.

Usually in class you'll just get a simple example to show the basic concept. Much practice is required following that.

Good luck.

[ericasaidso]

The reason teachers do that is to challenge the students who are memorizing problem to problem. They figure if you really understand the underlying concept that adding a slight change won't trip you up. It's not sadistic.

[76Neesa]

Your a sadistic teacher aren't you!

[ScotleCyphez]

@conman2317 or if you have truly learned and understand the easy ones you can use that process for a more complex one... they are testing to see if you actually know it.

great vid.

[Kael7777]

try the expanding cone lol

[flyingbeagles]

@conman2317 thats the point of math exam really. to filter out the people who really understand the concept and people who don't. people who don't try to memorize steps, people who do just manage it on their own

[adellaxx]

thank you so much!!

[slblondie2]

thanks, very useful

[phoenixm4]

Great video. You're a lifesaver, I just had a homework problem exactly like this with different numbers. So much easier to understand than my professor. Thanks a bunch!

[platanoproductions]

OO i see it sorry GREAT VID

[patrickJMT]

ok, glad u figured it out! : )

[platanoproductions]

how did you get h/2

[Nerdnie]

diameter= h

therefore,

radius= h/2

[cosm0]

awesome dude !

[iloveubutichoseddark]

yes. Just what i need it, cone problems!

We been doing related rates cone problems for the last part of the semester and i didnt understand a thing.I dont know why they like cones so much on the ap exams and books.. seriously, what is so intersting about cones? lol

[yarden123]

thanks man! just explained the topic to me in literally 2 minutes, when i couldn't understand my teacher for a whole semesterrrr

[patrickJMT]

i am your teacher now!

[hotsum0ta]

@patrickJMT Your school are belong to us? :D

[KillerTaco346]

I saw someone else use the equation V=(1/3)(pi)(r^2)(h)

However, instead of substituting (h/2) in for r, they substituted a 5 in for r (when h=10, r=5). Would this be incorrect. Well, I'm getting a different answer so it must be. You cant substitute exact values into the original equation right?

[cjy2k6]

dude you are the best!

[patrickJMT]

: )  thanks!

[RussianCosmonauts]

you just got me confused a little for saying we leave the pi over 12 alone, nevermind. Thanks for replying

[patrickJMT]

well, the constant just gets carried along when taking the derivative...

[RussianCosmonauts]

Don't you have to take the derivative of it or something?

[patrickJMT]

sure, and i do take the derivative!

[RussianCosmonauts]

Why do you leave the pi over 12 alone?

[patrickJMT]

what would like done to it?

[fruit123grl]

Thanks, this helped me for my calc test. (I also realized I wasn't using the correct formula...oops)

[patrickJMT]

ya, you got to use the correct formula! : )

glad the rest helped too!

[Waranle]

Thank you Patrick :)

[patrickJMT]

happy to help as always

[ImmortalBisonInc]

This helped quite a bit