Related Rates - Simplified

Related Rates: Easy how to process with a boat being pulled into shore by a winch.
7 more related rates examples at Calcworkshop.com
1. Air being pumped into a balloon
2. Conical tanks
3. Ladder sliding down a wall
4. Pebble dropped in pond
5. Edges of cube expanding
6. Radar tracking station and airplane flight path
7. Cone at sand and gravel pit
For another example on Related Rates visit:
Calcworkshop.com
SUBSCRIBE for Improved Grades ➜ www.youtube.com...

[@allanbarahona4657]

THANKS SO MUCH!!!! BEST CALC TEACHER EVER

[@Calcworkshop]

WOW - Thank You!!

[@ramichoeb2743]

My right ear thanks you

[@Calcworkshop]

haha - you're welcome

[@hoochiemamma2]

left*

[@aaronnibbe4567]

thank you so much for uploading this lesson. this was taught in a much more understandable manner than how my teacher taught us.

[@Calcworkshop]

Hey Aaron - thanks so much. Glad you enjoyed the vid. :)

[@Onnethox]

The first problem is the exact one i have on my book! Thanks

[@Calcworkshop]

:-)

[@trishacastillo4829]

You explained it very well! Thank you so much

[@soonerfan0161]

Smh I really wish she was my professor, my professor is trash😂

[@AceofDlamonds]

I love your way of teaching and I didnt know your videos were only weeks old.
The content dense teaching style helped me learn more about implicit differentiation from your three examples than my textbook + class in a week!@
Thank you.

[@Calcworkshop]

Hi V Ling, Thank you for your great feedback! :)
I'm delighted that you enjoyed my teaching style. I'm always thrilled when I see my students get that 'aha' moment when I'm teaching.
Yes, just filmed that a little over a month ago.

[@tunneltrance]

you wouldn't even believe it, I watched this video 45 minutes before my calculus 1 test and this was the exact word problem given! The numbers were different but this was exactly it. Thank you so much for this video it saved my life today!

[@Calcworkshop]

WOW - Now that's amazing!! I'm so glad it helped you out!!

[@adabujiki]

wow--- what an amazing woman.. you've helped me in a way i cannot describe

[@klyxes]

could you include more than 1 problem in videos like this? it's a good explanation but i think it would be better to include more problems so that the spectator can know whether he/she if beginning to grasp the info. correctly.

[@Calcworkshop]

Hi klyxes, thanks for the comments! I have another example for related rates on my site, calcworkshop.com. Look at the sample videos on the front page. :)

[@anabellalutz2312]

Please do another example of this! Your teaching is amazing!!!

[@Calcworkshop]

Hey Anabella Lutz - thx :-)

[@zifengjiang5899]

This really helped me thanks alot

[@rhenry973]

you are amazing!!! my calc teacher always rushes the lessons so i end up having no idea what im doing

[@Calcworkshop]

Hey +Rob Henry - WOW, thanks so much for the kind words. :)

[@1light4love]

I feel ya! Mine rushes and thinks everything is crazy simple... "just take the stuff of the stuff and multiply by the inside stuff but NEVER plug in the other stuff FIRST!" ....nowhere in there did he mention THERE WOULD BE A CONSTANT FOR ALL PATHAGOREAN APPLICATIONS!!!!! thank you SO much CalcWrkshp! I have a big exam coming up next week, and will be checking out tons more of your videos over the study-filled wknd! ^_^ Plz keep it up!

[@prissarpong]

You rock Ma'am!

[@Calcworkshop]

+Aminata Diallo :)

[@tedm.8572]

I like how you reiterate concepts in different ways.

[@Calcworkshop]

Hi Theodore Morrison - thanks! I'm glad you enjoy my teaching style. :)

[@Calcworkshop]

Related Rates Example: Basic practice problem for related rates in calculus. It's one of the many classic related rates problems students will see in Calculus I (AB).
A boat is being pulled into shore by a winch.
For more lessons covering all topics in Calculus I and Calculus II, visit Calcworkshop.com

[@cognitojames9694]

You are an excellent communicator. You have a way of making what use to be complex concepts, simple. Please continue, people like me need this type of teaching.

[@Calcworkshop]

Hi Cognito James, Thank you for the kind words! :)

[@abaytesfaye8266]

interesting i appreciate u

[@aaiilleee]

you saved my life seriously best calculus teacher ever!!!!!!

[@Calcworkshop]

+Ailee K - WOW - Thank You SO Much!!

[@jackross7459]

I'm in 8th grade math and I'm happy to hear the Pythagorean theorem isn't useless

[@Calcworkshop]

+Jack Ross :)

[@LawriLuvsLemonade]

Jack Ross Why were you watching a Calc video when you were in the 8th grade? 😂

[@Farrukhw]

Very Well Explained. You really rock Ma'am...

[@kristitruong97]

You have saved my life!!! Thank you so much

[@bjlouisRev]

This was awesome. Finally learning how to do this stuff with your help.

[@Calcworkshop]

Hey Bryan - thanks! Glad you enjoyed our video. :)

[@1nappy]

THANK YOU!!!!

[@mkayzondy]

Great video.....Thank you

[@rishabhuniyal9117]

This video is too good to clear my concept regarding this topic thank you mam.......................
Thanks A Lot

[@medinasFamily]

Thank you. You are the best! This video is so helpful.

[@Calcworkshop]

Thanks Luis!

[@abdiboru8983]

please teacher aploud limits and derivative lecture i love your teaching system

[@karah6165]

Hi! Just a quick question. Could you simplify 13(-4)/5 and have -10.4 as the final answer? Or do you prefer to leave it like "13(-4)/5"??

[@tacosamuel]

Karah O yes

[@smokingtires5]

Why do you only have 2 videos? I'm pretty sure there are more topics in calculus that need covered.

[@Calcworkshop]

Hi Kenny Krey, now that'd be a popular channel, "Calculus: Done in 2 videos!", right? :) Was there a specific topic that you were interested in?
If you'd just like to see what else I teach, then you can check out my site, calcworkshop.com, for my calculus course.

[@carolinemitchell5711]

You are super fantastic. Please put out more videos!

[@aschmitt5260]

This helped clarify a lot that I did not understand in class!! Definitely good at what you do, thank you!!

[@Calcworkshop]

Hi *****, Thank you for the kind words! I'm glad I could help clarify things for you.

[@Nate-oj4eb]

Shouldn't h^2 be = 2h --> then plug in the height? I mean there's still a power right?
also, r is just a number.. so shouldn't it be ZERO too? lol getting confused.

[@nightslayer380]

Nate R is a number but it's a number that changes with respect to time, since the rope length is changing. H is the height of the dock which doesn't change at all throughout the problem. Also whichever way you solve for h it is just a constant number which will always be 0 when you differentiate.

[@Nate-oj4eb]

fgdh

[@adv3nturetime]

so basically its because h isn't changing and everything else is, bro

[@OscarRodriguez-tr6tc]

why does the boat accelerate?

[@emmanuelapuamadi9591]

please when you take the derivative of b^2 why did you add db/dt and r^2 you add dr/dt. explain it please

[@TaraMenonPattilachan]

Emmanuel Apuamadi Have you seen her elaborate Implicit Differentiation video? You probably should if you want to know why. It's standard.

[@bahuleyan6552]

malayalMsX

[@gordonglenn2089]

Short answer: The Chain Rule
She is taking the derivative "with respect to time" in each case, not with respect to b or r, so she must multiply (not "add") by the inner derivative.

[@arpinemanukyan9458]

Great explanation!! Thank you so much!

[@Calcworkshop]

Arpine Manukyan Thanks! Glad it helped.

[@anticbruin4513]

H is just a number....

[@ultimateossas]

"age is just a number"

[@williamblake3795]

thank you so much:)

[@leebowlby]

Very good explanation. Thank you.

[@Calcworkshop]

Hey leebowlby - thanks for the feedback!

[@77moOoDy7]

You are amazing I really wish you'll keep going

[@Calcworkshop]

Hi Al-Mutawwa Mohammed - Thanks and I'll have more videos posted this Fall.

[@Serie56-69]

Thank you!

[@samraimi4265]

great vid, steps are very detailed! Post more related rates? ;D

[@Calcworkshop]

+Sam Raimi - thanks :)

[@aashishshrestha8180]

nice

[@Anubis10110]

love you

[@irfanshahidan9651]

the best teacher . thank you

[@Calcworkshop]

Irfan Shahidan :) :)