The Quotient Rule

[Vordrazz]

These videos are great! Thanks for the help! After passing first year calculus I thought I was done! Unfortunately you need it to set up and monitor thermodynamics in physical chemistry haha.

[Poiboyification]

i honestly do not get how this is going to help me in the future... -_-

[patrickJMT]

@Poiboyification it probably wont

[Poiboyification]

@patrickJMT thks for the inspiring motivation..

[patrickJMT]

@Poiboyification no problem.

[Proman155]

Hey der....me from india ! thumbs up if u feel PatrikJMT is better than ur professor !

[jchen0011]

Thanks a lot for the help. Go become a professor!

[patrickJMT]

@jchen0011 you are welcome. and : no thanks : ) 

[firefoxx46]

Thank you Patrick. You are the greatest . Cheers.

[Red1Storm]

In my calc class we say ho instead of low. Much easier to remember because there is a ho on every corner.

[kimzisk3wlz1]

YOU'RE THE MAN

[fhansea]

My teacher taught us that mnemonic, but instead of "low-low" she says "square the bottom and away we go". Same concept, but I do appreciate yours being shorter in words!

[randompersonB]

Lo, d-high minus high, d-low over low-low? Sounds like fighting game annotation

[TheLastStand2009]

Thanks man, these vids are great for going over work I've learned in my A Level class :)

[WhiiT3Rabbit]

WTF you didnt even simplify it?? what good is that

[m3talm0nst3r99]

@WhiiT3Rabbit You should already know how to simplify that imo.

[TheDee032]

If you were my calc teacher I think I would actually enjoy class. My teacher rambles and throws definitions around all day. You are the God of Mathematics!

[dragonflar8]

Dow we have to memorize the derivatives of the trig functions

[jhademcconnell]

I missed class due to a field trip and you've put me back in place :D

[Flovust]

Hey patrick i need some help, got a quiz tomorrow, and I cant seem to get this question right

√(2x^2 + 1) / 3x

could u please do a step by step...

[zadavidson]

My high school calculus teacher minored in poetry. This is what he taught us to always remember the quotient rule, "Low d, high. Minus high d, low. All over the square, of whats below." I haven't forgotten it since!

[TheMooee]

Just told my professor about you. Wonder how this will go over tomorrow when I'm in her office...

[patrickJMT]

@TheMooee well i guess it depends on how you said it. if you were like: ' hey there is this nice free resource out there that maybe some of your other students may also like' , she will probably be a-ok. if you were like: hey, you really suck and the only thing that is helping me pass is this crappy class is this kick ass guy on youtube ' she will probably be a bit less excited to see you. : )

[TheMooee]

@TheMooee Lmao, well it was more like the former, but she actually ended up giving me links to other sources? Hm...

You are indeed kick-ass though, my good sir.

[lpfanlord123]

couldnt you use L'Hopital's Rule?

[darkangelic88]

hi patrick, can I know if it matters if this applies throughout for specific numerator and denominator? e.g. numerator must contain constant/variable and denominator must contain constant and/or variable?

[patrickJMT]

@darkangelic88 u can use this rule for any fraction

[darkangelic88]

@patrickJMT thanks Patrick!

[LeutArtemis]

easier way to remember is:

y=u (over/divided by) v

y'=vu'-uv'(over/divided by) v^2 (v squared)

Sorry if it is hard to understand but this is the best I could do on the computer.

Basically you're just substituting the complicated stuff on the left of the = sighn with a "y" and stuff on the left with "u (divided by) v"

It just gets rid of all those brackets and f's that you just don't need, it renders them useless and is MUCH easier to remember.

[TheNumber2Pencil546]

Low D-High minus High D-Low over the square of whats below. that how i learned it too haha

[TheMooee]

@TheNumber2Pencil546 Holy frick... That actually worked. I may love you now.

[bennybong360]

u have amazing writing :)

[anime4lifeyo]

Why don't you finish the examples you gave ?

[poyanator]

you should be the international minister of education!!! holy crap you say things sosoosososo straight forward! text books use a shit load of confusing and unnecessary letters for formulas and set examples out really retardedly!

you did it perfectly!

[shraddhasunil]

You're videos are amazing....thanks so much for all these videos...they help so much!

[despicablerainier]

@patrickJMT ur the best :))

[paomolina]

I have a question when u distribute the tangent and secant square at the end what would the answer be? I got sec^2(x^3/2)+sec^2(5x)-3/2tan(­x^1/2)+tan(5x) all over (x^3/2+5x)^2... I have the feeling that I still have to do something else, but idk...... Thanks!

[mjsm111]

one thing bothered me >> how can you solve this by left hand !!!

[Theloza09]

i got a 91 on my last test because of this video thanks man!!!

[MrSgoodspeed]

Marvelous, you are marvelous! Thank you so much, wish me luck on my final =)

[gurngurn00]

I like your marker :3

[plugee]

OMG I do not care about Mormon Scientists!!! STFU ADS!!!

[FuNnYmOjOoO]

how do u know tan becomes sec?

then whats sin and cos

[exscape]

@FuNnYmOjOoO Pretty much memorization. You can prove the derivative of tan(x) relatively easily, but you need to know quite a few trig identities and either the product rule or the quotient rule.

[mayz5293]

THANK YOU SO MUCH FOR THIS!!!!!!

[XNightfallX8]

I have never liked doing math, but there is something about your method of teaching that makes me enjoy doing these problems. Thanks man you rock !

[dajakesta1234]

im gr 9 and i understand this thanks prof patrick

[tailblaze101]

Noo, it's: Low D-High Less Hi D-Low and underneath the square will go XP

[09mvsu]

I love you...THANKS FOR THESE FREE VIDEOS..I AM CURRENTLY TAKING TRIG AND CAL IN COLLEGE AND I WAS PULLIN MY HAIR OUT TRYING TO FIGURE OUT WAT AND HOW TO DO THESE PROBLEMS TIL I FOUND YOU ONE DAY AND ITS ALL FREE HELP! MY TEACHERS GOES TO FAST IN CLASS SO WHEN CLASS OVER I JUST COME TO MY DORM ROOM AND CONSTANT REPLAY YOUR VIDEOS TIL I GET IT! THANKS SO MUCH!!!

[MendoBud640]

great video, thank you very much for posting and taking the time to help others.

[bbortz]

Just a thought--it might be helpful to some viewers to have a video showing the derivations of the derivatives of trig functions.

[Zombiefruit]

MOVE ASIDE JESUS! PATRICKJMT FOR OVERLORD!

[jacquezmin]

your teaching skills are epic.

i never understood it the way my prof did the talking.

thank you so much!

[mongoose308]

Thanks for the video. The mnemonic device was alot of help. (^_^)

Thanks for saving my academic-mathematical life over the past 2.5 years lol.

[Splooshiba]

thanks very much, these videos are brilliant for revision

[Cervclash]

Thanks for the help, my brother referred me here.

is that the final answer? @3:39

[wazzerfc]

you sir are a living legend !! you have helped me more in these 7 minutes than my lecturer has in 2 hours !! thank you soo much !

[PoonJavie]

f(x)= high

g(x) = low

d = derivative

Low d high minus high d low, draw the line and square below.

[mrosendal]

Thank you for doing this, i hope you make a lot of money on the ads you really deserve it !

[mattsmurfy]

Sharpie!!!!

[TBBuccaneers1717]

I... I love you. I have an exam in 5 hours and was kinda frantic because I stupidly never attended class.. But you explained this so nicely

[lando30001]

just plug it in

[KevothatGuy]

omg i love this guy, i have a bad teacher, so i never understood this. thank you so much

[hosephollywood2]

i cant beileve how good you are at this!

i mean my teacher does his job well but this really helps to solidify the concept in my mind:]

LATE NIGHT MATH REFERENCES FOR AN ASSIGNMENT THATS DUE IN THE MORNING FTWWWWWWW

[gsronde26]

OMG thanks so much for loving math.. and taking time to teach me n other.. MAJORLY HELPFUL :)

[EdwardManeikis]

You, sir, are a boss

[DJCrabCake]

MOVE ASIDE OBAMA! PATRICKJMT FOR PRESIDENT!

[patrickJMT]

@DJCrabCake ha, i would not want to be president ever.

[blutch222]

@patrickJMT don't you get it, DON'T YOU GET IT? you don't have a choice sir!! this is a democracy, if WE want you to become president, YOU WILL become president end of story

I think there's some major flaws in what I said but whatever...

[solidwolf52]

learned more from a few of this guys videos than i have from my math teacher in the past month. more teachers should be like him.

[12kate34]

Thank you so much!! I actually feel like I have a chance of passing the AP calclulus test now :)

[skyyrocketaway]

A lefty! =D

[RedTearS88]

love you

[crazieh00]

hellow.. plz solve this:

f(x) = 4x / x^2 + 1

[caroleabumoussa]

@crazieh00 It's (denominator times by derivative of numerator) minus (numerator times derivative of denominator) all over (denominator squared).

That is,

f'(x)=((x^2+1)(4)-(4x)(2x))/(x­^2+1)^2

Multiply out:

f'(x)=(4x^2+4-8x^2)/(x^2+1)^2

Simplify (notice that 4x^2 - 8x^2 becomes -4x^2):

f'(x)=(4-4x^2)/(x^2+1)^2

My professor doesn't care if he bottom isn't multiplied out. I don't know about your professor.

Anyway, hope this helps.

Reply again if you have more questions & Keep watching these videos!

[yadirawc]

wasn't the 1/2 exponent on x be negative? becuase you subtract 3/2 -1?

[richynero]

cheers matey!



[sandra17143]

infiniti+1 thank yous! i thought i was doomed!!

[XgtkidX]

you sir, are good at what you do!

[DaGr8Gatzby]

You are a god among men.

[ARabidSquirrel42]

Thank you so much. You are exactly the kind of teacher that helps me. Keep posting these, you are saving lives (and GPAs).

[f1tzy0]

thanks very much all the other stupid websites crap on about stuff, and u get straight to the point and showed me how its done propally. thnaks to you my assignment should be good :)

[Achooification]

Your videos matter a great deal. Thank you!

[MasonMurdock]

Thanks a lot patrickJMT, very informative. I also use that pneumonic piece to remember the quotient rule but I say, "the square of what's below." Because the low-low looks like (g) - (g). 

[kupop0w]

thank youuu :)

[rose14x]

thank you for the help! Exam in less than 24 hours

[flejkso]

@rose14x

same! in 3 hours :O

lol, all good, thanks to these videos :)

[456crows]

thanks so much

i have my leaving cert maths in a few hours and you saved my ass!

[TheNinjassin]

fantastic videos, thank you very much for your help... I can imagine it would be very rewarding to have you as a teacher...

[dcourtn1]

you are great.

thanks for taking the time to help us all.

[patrickJMT]

@dcourtn1 no prob

[mrhe832]

@patrickJMT

It seems like the quotient rule is the exact same as the product rule, however the division of the denominator squared is the only difference. Is this correct?

[mypinkdollprincess]

I didn't know that people like you could change the world under 10mins!! Thanks a Zillion!

[mypinkdollprincess]

Hey, thanks again!

[mypinkdollprincess]

I didn't know that people like you could change the world under 10mins!! Thanks a Zillion!

[vedvishala]

an entire semester's work couldn't help me like your vids do..................thank you so much.

[patrickJMT]

@vedvishala no problem at all

[tsfarnoudi]

OMGGGG YOU ARE AMAZING I LOVE YOU! lol why can't all professors teach like you! thank you!

[patrickJMT]

@tsfarnoudi my pleasure : )

[xpenguino974x]

THANK YOU! I have the AP calc exam tomorrow, and your videos are great review for everything I've learned throughout the year! Short and sweet! You're a life saver!

[pimpinAnn]

What the fuck !!!!!! I must b dumber than I thought, I don't understand a GOTDAM thing these videos are supposedly explaining. Nor do i think, or at least hope I will ever need to understand this kinda crap...!!!!! Furthermore, I believe sometimes people of less intelligence are just happier people. And you guessed it,,,,, I'm happy as SHIT!!!! no disrespect to you who need this stuff ,,, just don't run me over when your trying out your new Lamborghini's

[ian8206]

@pimpinAnn That's a matter of opinion really. Are addicts really happy? I met my current girlfriend of over 2 years going to post secondary and I couldn't be happier :)

But there is a crap load of stress I'd like to be without, I won't deny that.

[VizardDLim]

thanks alot patrick..im just about to to study calculus...and this tutorials is helping me alot daaaaaamn rock on man \m/

[andrewnagi]

i find a simple way to remember this rule is [square it, put it] this is ofcourse referring to the denominator, and after you remember that and the fact its minus on the top the rest is easy enough to figure out! Great vid thanks!

[MasterKiraX]

Thanks for that little rhyme! I love stuff like that, it helps me more than seeing a bunch of g's and x's.

Lo, D-hi minus high, D-low

[AtanasNenov]

Awesome vids!

One question about the quotient rule though - why did you swap the places of f' and g' as opposed to the product rule? It's the same thing, with the second factor being of power -1. It's a lot easier to remember the quotient rule being the same order as the product rule, i.e. derivative of first "factor" (i.e. the numerator) times the second "factor" (i.e. denominator) unchanged minus first "factor" times the derivative of the second "factor" and ofc over the 2nd "factor" squared.

[tomczyce]

I have a question.

Why does the rule specifically reverse g(x)f(x)' into f(x)g(x)' . What is it's sifnificance? Thanks

Ps. Great videos. Keep em coming.

[tomczyce]

Question:

Why is the g(x)f(x)' reversed after the minus into f(x)g(x)' ? I don't see the significance of it.

Thanks . And great videos. Keep them coming.

[niel423]

Thanks.

[DarkKitten878]

A student from Western Michigan U is in your debt. My prof here sucks a lot!

Thanks.

[tom123ek]

(f/g)' not f/g

[Lakers1star]

This guys has saved my twice!! A student a Virginia State thanks u

[julietterfly]

You should be submitted for sainthood.

[eishambade]

thanks that really helped a lot .even my teachers dont get me understand all this so well.

[SoulRebelXII]

thank u

[zoemstof]

LEFTY. Nice.

[Liliprincess07]

OMG ur awsome, my second teacher.

[yjoshez]

crap this makes no sence for me

[bigdayowzyou]

hmm... I wonder why?

[iMNice99163]

Your still the man!

Go Cougs!

[budgiebreder]

i like the "high low" way to remember it thx!

[davvillers]

down(deeup) - up(deedown)/ downdown

dee is derivative

[karlkarlkarl1234]

The best way to remember quotient rule is simply:

( u / v )' = ( vu' - v'u) / v^2

So simple to remember; where ' is obviously the derivative.

[sadeyesace]

DN' - D'N / D^2

[passionatx]

welldone !!! ::) cheerzz

[krazikatt123]

Yeh, is that possible patrick? See the question below...

[rcabbage789]

I would assume you can times it out but I have been told for my exams that its unnecessary???

[77777computerperson]

hey patrickjmt is it possible to simplify that first quotient rule derivative at 3:40 anyfurther ? and if it is possible can you just give me the answer, also thanks for posting ur vids they are very helpful.

[karlkarlkarl1234]

Yes you can foil the numerator out if you want to to get:

(-3x^6 - 5x^4 + x^2 - 1) / (x^5 + x)^2

Not sure if you would have to do that in an exam, I just did it to look for any common terms or canceling. In my maths class (1st year university) you are meant to do this where possible.

[77777computerperson]

@karlkarlkarl1234 thx u for responding

[thegoodmanhimself]

poop

[mizzmya2008]

i'm glad you have neat handwriting!!!

[jajaja295]

I have an exam in 18 hours, I wish I found you sooner than half an hour ago :( ... You have helped me so much more than what Ive been paying in tutoring all year

[12345678910mikey]

thank you so much. I aced my test cause of you! and my teacher doesnt explain it well at all.

[LuckyCharms432]

Thanks dude, not everyone gets the best teachers or can absorb this in class right away. You're really helping me out.

[JoseRaul78897889]

dude, thanks for this type of videos... i was just curious and searched calculus tutoring in youtube, and found this and a couple of more videos.... and i'am really glad that people take their tame to help others, you just don't see this too often anymore....

keep up your work, even thought i didn't needed this, I am sure many do need it.... cheers

[theonlycoolone]

Thanks very much man. You're doing a great thing and helping many students like me who need a little extra on the side to learn things. I have a quiz tomorrow, and I am now feeling confident! Thanks again!

[marcusjhung]

You know that is a really cliche excuse "we'll never use that in real life...blah blah blah". People who think that are really dumb. Almost all math learned in school can be pragmatically applied to field of all sorts...unless you're gonna be flippin' burgers your entire life.

[bhenedick]

I also heard that mnemonic device of your student to our prof. and when I first heard that, I was confused how to use that. thanks for explaining it up further.

[riverduck3]

You will never need this crap in real life. Why do schools insist on torturing people with this stuff?

[patrickJMT]

you can that about most everything you learn in school...

[Rovhatt]

@riverduck3 I WISH I'd been taught "this crap" in school - turns out I need it every day "in real life"

[D4v1id]

At 2:25 you put the problem down correctly but then put an equal sign inferring that it is equal to the derivative! You need to start a new line there and put dy over dx.

[badstorm666]

Thxxxxxx :)

[patrickJMT]

my pleasure : )

[0412coco]

thanks so much - sitting my leaving cert tomorrow (in ireland) for maths and u have been a life saver :)

[chuuzz1]

Nice little refresh for my exam tomorrow, lol.

I'm so lazy, lol.

Good work, if only I found you sooner....

[Jabed21]

awsome quotient rule! now i understand chain rule, product rule and quotient rule

[weeman5872]

Ditto :P

[Ridin24z]

Awesome =] many thanks from the UK :P

[Angeline422]

Thank you so much!... Cherrs from China~haha

[iamashooter]

liar! youtube is banned in China

[Angeline422]

Hey... U R not that friendly, I am a Chinese, that's why I said cherrs from China, but that doesn't mean I live in China, I live in Nederlands, thank you.

[danlyomil]

[low d(high) - high d(low)]/low suqared

[Zhangsiping]

Cheer from Canada!

[aikoromero]

Thanks a lot!

Greetings from the Philippines..

[fikre1990]

thank you a lot. It is extremly helpful when i was preparing for exam. God bless you.

[napster428]

Thanks, This helped i missed my class and this what they did... so thanks and keep up the great work all the way from CANADA

[chopa12]

Nice thanx. Cheers from Puerto Rico :p

[jinukaqo]

Thank you!

Greetings from Accra, Ghana!

[patrickJMT]

wow ghana!

it is amazing to see how people all over the world are watching these!

it is ironic: some boy from the backwoods of kentucky is spreading math cheer all across the globe.

i am the santa claus of mathematics

[javagao]

helped a lot! exactly what i was looking for...

Cheers from Brazil

[cmrules]

Get the quotient rule, crap at simplifying the answer though!!

[kirt18]

the video is no longer available???can u upload again?pls

[muskaanrocks21]

Thank you very much!! I usually watch your videos before my teacher teaches the lesson!! ur great!! keep it up

[rosh352]

your a life saver.. thank you

[HeyWheresKel]

This is such a great help, but did you ever consider making a video of harder things like finding and factoring/simplifying second derivative of functions that require Quotient Rule? That would be totally awesome since it's what I have to deal with and I'm sure others do too.

[patrickJMT]

i may do one this weekend... someone else asked for something similar (mainly the factoring part) - i will do one this weekend probably!

[PhilMarl]

your the men thanks for the video u really help me alot ;)

greetings from vienna austria europe

[patrickJMT]

ohhhh nice! vienna!!! my wife got to go there for a math conference once, and said the city was so totally amazing. i would love to visit : ) if i ever come, you have to give me a free tour of the city in return for my services to you! : )

[arhwhyayehn]

patrick great tutorial! Easy to follow and understand! Thank you