Introduction to Related Rates

This calculus video tutorial provides a basic introduction into related rates. It explains how to use implicit differentiation to find dy/dt and dx/dt. It contains examples on derivatives and related rates.
Introduction to Limits: • Calculus 1 - Introduct...
Derivatives - Fast Review:
• Calculus 1 - Derivatives
Introduction to Related Rates:
• Introduction to Relate...
Derivative Notations:
• dy/dx, d/dx, and dy/dt...
Related Rates - The Cube:
• Related Rate Problems ...
__________________________________
Inflated Balloon & Melting Snowball:
• Related Rates - Inflat...
Gravel Dumped Into Conical Tank:
• Related Rates - Gravel...
Related Rates - Area of a Triangle:
• Related Rates - Area o...
Related Rates - The Ladder Problem:
• Related Rates - The La...
Related Rates - The Distance Problem:
• Related Rates - Distan...
____________________________________
Related Rates - Airplane Problems:
• Related Rates - Airpla...
Related Rates - The Shadow Problem:
• Related Rates - The Sh...
Related Rates - The Baseball Diamond Problem:
• Related Rates - The Ba...
Related Rates - The Angle of Elevation Problem:
• Related Rates - Angle ...
Related Rates - More Practice Problems:
• Related Rates - Conica...
_________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Next Video: ruclips.net/video/7BK_mmYckmI/видео.html

[@unknownnigga3679]

Ty!!!!!!!!!!!!!!!!!

[@khabibmusashaykhov7811]

umm excuse me, where is his Nobel peace price, math prize, MVP prize? This man deserves it all

[@Boog1137]

Psa: the maths analog to the nobel prize is the fields medal

[@abdoulazizdabo9064]

Indeed!

[@knora2974]

Why is it that in the first problem, y=+/-4.
But in the second problem, z=17, and not z=+/-17?

[@elaxter]

@@knora2974 He said "to keep things simple"

[@900k.]

cringe

[@efass6289]

This man has been my messiah for Honors Algebra II, Honors Pre Calc, AP Calculus I and II, Honors and AP Chemistry, and AP Physics... I stan
Thank you so much for all of your help, I am now going to Cornell as a double major in math and computer science. I honestly think my understanding and love for math has greatly been facilitated by your videos, and I plan to use your videos for college and beyond!!

[@brouncruiser]

congrats man

[@keanaleong7745]

Well done!

[@davidedmundtochi5228]

Only Jesus is your messiah bro.By the way , congrats.

[@thezapper130]

@@davidedmundtochi5228 Damn thats some cringe shit. People that are obnoxious about their own little cult are fucking annoying, take the hint.

[@davidedmundtochi5228]

@@thezapper130 I don't even really understand what you are trying to say. Try again.

[@edwardduda4222]

I'm literally in a breakout room and no one has any idea what we are doing. Thank you. You're my secret weapon.

[@aaronbaraiya3692]

lmao

[@top_ten_secrets]

i noticed on 4:42 that it was supposed to be -42 not 42 since you moved it to the right

[@ryanm6004]

You ended up doing the exact problem I was stumped on in this video, which really helped since as soon as I understood I could pause, finish it myself, and then feel the satisfaction of watching you do the exact same steps I just did and getting the same answer. Thank you so much man, your channel has been a godsend for all the stuff my teacher has pretended to teach me

[@illu653]

Thank you for taking the time to create this content and upload it to RUclips. I have had a difficult time understanding these problems as they were introduced to me in a complex demonstration of examples like filling a cylindrical tube at a rate of this an that, I never really developed a concrete understanding of how to go about the problem until now. You are helping propel students to a higher level of understanding and ability, so again, I appreciate your work and thank you

[@fsxaviator]

*Clicks on Organic Chemistry Tutor video* *Turn volume knob up to 11*

[@studiouslycozyniche]

I am so glad to see I am not the only one to think that this mans videos do not get the credit they deserve. I am with everyone below. I have watched so many other videos but without fail, every time I watch his videos, I will always finally understand a subject I was not grasping. He truly has a gift, the most amazing teaching skills! Do not let the length of some of his videos fool you, they are all jam packed with info and tools that break things down and teach you exactly how to do the subject. He is by far one of the best if not the best!!

[@garrettwilson3032]

This man has carried me through honors Chemistry, Algebra 2, College Algebra, Pre-calc, General Chemistry 1, and now Calculus. I would usually never consider patreon but this man deserves my money.

[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for an exceptional video/lecture on The Introduction to Related Rates in Calculus One. In the past, I had some difficulty understanding Related Rates problems, however my skills have improved with practice. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.

[@narumi650]

This dude helped me more than our calculus teacher.

[@nicolarryobbus6865]

This channel had helped me many times now. the problems that were used as an example were very similar to what is in my textbook and this has helped a lot since my instructor always base the tests on the textbook. I got an average of 98 in basic calculus this midterms and i really must say that this channel had a massive contribution as to why i achieved that grade. THANK YOU SIR FOR BLESSING US WITH FREE QUALITY MATH RESOURCES!

[@keeping_it_real]

Words are insufficient to tell how grateful I am to have found this channel... Man our lecturers expect us to understand everything by Instinct...

[@owenedwards2196]

You are the best teacher I have ever had. It is amazing how you make a concept whether it be Calculus or Chemistry that I used to think was impossible seem easy and simple. Thank you so much. You do not realize how much your channel has helped me.

[@celinabhandari]

ur saving my grades thank u SO much

[@R94jax]

I love you... and I say that in the most non weird way possible...

[@fartsniffer9999]

you are carrying me through my calculus class 🙏🙏 i cannot thank you so enough man, you're a miracle for all of us struggling students out there

[@maryam4587]

5:10 I was like dude I should go back to middle school but thank god I was right. Thank you very helpful video.

[@connerrad321]

Girls: omg why isn’t he taking my hints
Their hints:

[@sahitibobbala5581]

HAHAHA

[@JS-ns8dr]

🤣🤣🤣🤣🤣

[@mordecai8707]

Women been on that super brain stuff since the beginning of time.

[@ARTDEVGRU247]

i don't get it

[@mrsryoukotakihama]

thank you so much, my teacher didn't really explain as nicely as you have. you explain it in such a way that it's a snap to understand

[@connorferguson6384]

At 5:00, when it says 42 + 8dy/dt = 0, then the next step has positive 42 on the right side, would you not have to subtract the 42 from each side to get -42 getting a dy/dt of -21/4?

[@connorferguson6384]

nvm lol didn’t get to the part where you corrected lol

[@kingbram8965]

@@connorferguson6384 just saw this problem too LMAOOO

[@sibusilehadebe1314]

i saw it too

[@_-_-_-_-_-_-_-__-]

whoever invented related rates has caused the dismay of so many students

[@miguelconfesor4701]

The organic chemistry and khan academy are two of my favorite channels in learning maths

[@mach2677]

This man is the cure to my math headaches!

[@ahterajones2121]

I can say I’m actually good at calculus I can understand I’m the first in my family to say that thank you so much you are a wonderful help organic Chem tutor❤️

[@isaiah9077]

I watch these videos before I go to class just to flex on everybody...

[@ARTDEVGRU247]

My calc professor actually just has us watch this guy's videos before class. haha

[@into_abyss]

😂

[@tully4595]

Idc what anyone says you the GOAT for math tutoring on RUclips. Thank you my g 🙏🏽

[@goshbaby8531]

Mashhallah you are very knoweledgble in explaining, i have learned so much from you lol. May you have the ability to learn more

[@michaelharris1884]

Best Tutor on RUclips!! Thank you so much 🙏🏻

[@iluvminecraftO]

bro is a God of sciences

[@shirinsidharta6995]

Thank you! I would have never had gotten this far in calculus without your help

[@deepfriedavocado]

IVE BEEN BANGING MY HEAD AGAINST THIS FOR A WEEK, THANK YOU SO MUCH

[@santiagocalderon-rueda6096]

You make everything a lot easier to understand. Thankyou!!

[@rhyymin]

I love you Organic Chemistry Tutor, you're carrying my calc grade for real

[@darshanghimire8248]

at 4:50 you almost got me so good lol!! i thought you made a mistake but you corrected urself. Attaboy!!! :)

[@pedrooreosg9180]

I have a test tomorrow and a fever, thanks man for doing these videos

[@yeeterskeeter1577]

must be a good feeling when you look at your comment sections filled with compliment eh?😁😁😁

[@zuhairreza]

Hahaha thought so too... Well, he deserves it!

[@sebastiancurry3714]

My boy, you got me into the engineering program at my dream school. Textbooks cant teach shit, im using your vids to pre study my first year of engineering, semester comes up in a month and I already understand all the physics and math classes to a reasonable extent and I haven't even started school yet

[@TheInvisibleOne1026]

How’s it going so far?

[@sebastiancurry3714]

@@TheInvisibleOne1026 Made it through first year of engineering lool, it was absolutely fucking brutal LMAO. Got hit with a hefty ass work load, but I worked my ass off and passed everything. Was holding on by a string though, but I think I managed pretty well considering im into bodybuilding, was able to get through it while still working out and doing other things. Funny how I thought preparing in the summer would make it hella easy, BOY WAS I WRONG. Honestly the most stressful year of my life. But for my university atleast which is top 5 for engineering in canada, they say first year is the worst year, only need to worry about passing. Had to work my ass off just to pass, but its worth it. Just dont ask me to repeat that hell hole of a year again omgg so happy its over. Time for second year after this summer break.

[@TheInvisibleOne1026]

@@sebastiancurry3714 Keep pushing brotha, do or die!! Lol. Thanks for the reply, I can relate!

[@simonphoenix3789]

I am so thankful for this channel... I can't believe how terrible our textbooks are at explaining anything. I learned more in the first minute of this video than I did from two and a half hours worth of class time and reading our crappy online textbook over and over again.

[@bowwow4893]

everything just clicks when you explain, thanks

[@paimanmartin5154]

You're the best my brother ❤

[@AbdullahAlharbi814]

mr you are a legend

[@charles-qm4ss]

This guy is the real MVP!

[@statik8460]

I needed this, I have a ap calc ab midterm today, what a blessing, ty very much

[@omgupta1857]

Related rates problems are amazing to solve and these problems are interesting as a high school student.
Thx 😍😍

[@johnnolen8338]

"When z is positive seventeen ..."
In the given instance there is no reason to consider z = - 17 as a legitimate solution to the Pythagorean identity; z is the hypotenuse of a right triangle, both of the legs of which are positive. IOW even the reference angle of the hypotenuse is positive. Minus seventeen is extraneous.

[@thobanizitho]

thanks for everything man. U explain things so thoroughly

[@yesaketeshome9968]

Everytime you help me get unstuck with a homework problem I go ahead and leave the video playing all the way through even through the ads in the background. Im still a broke college student so hope that helps.

[@litchfirmian7562]

I can not explain how grateful I am

[@divinest]

4:45 its meant to be -42 not 42

[@Rob-J-BJJ]

he fixed it smart guy

[@DavidPerez-se4lz]

Thank you for your service, Organic Chemistry Tutor.

[@badbish6664]

honestly this man is the reason why im passing calculus. i’ll give u my firstborn

[@johnnoemartinez6233]

lmao, i just watch first 4 minutes, then I get it. you're better than my teacher.

[@michaeltian]

Took me an hour to do one question on a test on this stuff and my teacher was chill and let me finish the test tomorrow. Guess I better not disappoint 🤦‍♂️🤦‍♂️😭

[@chickencutlet3]

Legend. I’m cramming so hard rn

[@Samir-rd8xp]

Chicken Cutlet for ap exam ? 💀

[@chickencutlet3]

ImThatOneGuy shoot I didn’t see this but yeah for AP 💀

[@ranch3727]

why is this so simple, my professor makes it seem soo fucking hard

[@razasyed575]

we love you organic chemistry man

[@randommonkey4900]

you're 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000x better than my calculus teacher

[@Yarncarril]

This guy is my hero

[@gevenaowl1574]

u totally SAVE my life!!! Thks

[@colinsoileau5033]

Man, I remember back when I took calculus 1 related rates was the most confusing thing in the world. Now I’m working with matrices and Laplace transforms every problem and this shit is cake compared to that.😂

[@hayleywarner2219]

you are seriously my hero

[@jeremygraham7976]

I learned it on the first video your videos are awesome

[@TheDankDev]

Man u explained this so well

[@Di7s]

Thanks from Saudi Arabia

[@thegracegong]

JG stands for Just Great because his videos only be great!

[@johnbowman9734]

Thank you sooooo much!!!!! Your videos have helped me out very much!

[@hennanoor6346]

Thank you for your mathliness

[@profgray]

what's dx/dt if x = 9 and t = 3 and how does it work ?
d9/d3= 3? 😅...

[@luce9264]

that's not how it works...

[@cecehenry437]

i love this man

[@munisailkhomova9266]

Thanks for your videos.

[@joshhouchins8289]

How come you evaluated just 17, and not plus or minus 17, when solving for z, on the very last problem, but the problem before that, you did evaluate for the negative number?

[@taylormalfoy3233]

I’m literally in love w u thank u for this

[@ilkeuyankerstudent5347]

SO THANKFUL FOR YOU

[@albertandguitars]

Wow you helped me so much

[@hexpect]

you are the best

[@Kevin-rk4qu]

on the second problem, should z = + or - 17 instead of just 17?

[@christinanguyen1220]

i thought it was gonna be +/- 17 because we took the root of it but no one seems to be correcting it so im not too sure. i did the work for but it was turned out to be +/- 99/17

[@itsparker7124]

When you found z, why wouldn't it be -17 and 17 since you took the square root there should be two possible anwers, -99/17 and 99/17.

[@electricalnoobject5011]

Sir, you are my Idol ❣️

[@andrewkaldas9335]

You the man, man!

[@christinajacobe6151]

Thanks,very helpful

[@abdulmalekalasswad6340]

i cant thank u enough bro

[@ARTDEVGRU247]

Mistake in question one: It should be 8dy/dt= -42, not 8dy/dt= 42

[@sadi_supercell2132]

4:45 it should be negative

[@dayanajimenez3948]

thank you for the help

[@saberspeed77]

My calculus teacher should've started with this video and not a packet with word problems.

[@SwoggersLOL]

at 7:45, isnt it supposed to be +-17?

[@seanmartinez50]

Another banger video

[@sarahmahmoud1857]

Wait, at 4:39 , why didn't you change the sign fo 42 after you changed it's side?

[@scarffed481]

Same

[@babs8233]

thank you

[@mattstupet3]

I understand how to find derivatives, and know how y^3 differentiates to 3y^2. But then you say it is times dy/dx and I'm confused. What is dy/dx and why is the derivative time that?

[@_RIBOT_]

You are my hero

[@ShyShySchullie]

Thank you.

[@owens2703]

I'm sorry for the ignorant question as someone new to this, but what is the difference between joining and subscribing?

[@veevids2679]

You're a really great Math teacher. Are you teaching professionally tho?

[@donaldtrump8166]

My professor is wasting my time. He could've just explain me like what this guy did

[@rexcelillana7756]

first example was wrong it should be negative 42 if you transpose it

[@laimino]

he did mention it

[@dako8083]

Clearly you don’t pay attention much, he fixed his mistake

[@thegracegong]

My saviour

[@peaqsnsuresearch2339]

ur amazing bro