Related Rates in Calculus

Now that we understand differentiation, it's time to learn about all the amazing things we can do with it! First up is related rates. Sometimes the rates at which two parameters change are related to one another by some equation. With our newfound understanding of implicit differentiation, it's not too hard to find this precise relationship so that we can do important scientific calculations. Check it out!
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My final is in an hour

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This makes me feel better. My test on derivatives is in 17 hours.

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Well, fuck... I'm in the same situation currently... My final is in 24 hours from now...

[@final8146]

I'm a college student, this is one of the best math explanations videos I've seen in my life. Great Job

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Yeah I’m cooked

[@annas9016]

You saved me. This makes so much sense. Usually my math teacher is great at explaining, but I could not get related rates for the life of me. I can't believe it makes sense.

[@onyxignites2818]

3:29 For anyone wondering, there is an alternative way of solving this problem. Instead of isolating "(dr / dt)," you could have simply plugged in the values there, which would have given you *100 = 4π[25^(2)] (dr / dt),* which simplifies to *100 = 2,500π (dr / dt).* Isolating (dr / dt) gives you *(100 / 2,500π) cm./sec.,* which simplifies to *(1 / 25π) cm./sec.* PS: I had to comment this on an alternative account because Dave blocked my main account from commenting on his channel.

[@schl0ck]

I know it's been 6 years but I just wanted to let you know how much these videos have been helping me recently. Thank you for making this easier to understand!

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This is probably the only channel where one can want to continue learning new concepts. Waiting for the next.

[@ProfessorDaveExplains]

that's the best kind of compliment! thanks kindly!

[@Amit-yf9ft]

You are incredible. Some feedback: I love how you speak clearly and slowly. You pause at the best times so that we can process and take notes. You explicitly explain not only the process, but WHY and HOW this all makes mathematical sense. Thank you so much. My AP Calc teacher is amazing, she really is. It's just that after a long day at school it is hard to remember and process everything. I view this as a supplement to my learning process in Calculus (one of my favorite classes)

[@layla229]

How was your ap calc??

[@lightning77125]

Same with me, my calculus teacher is incredible. But whenever I'm at home, ready to do an AP Classroom assignment that's 35-60 questions long, these videos are the perfect way to refresh my knowledge of the concept and make me ready for anything.

[@DBear8008]

I took AP calc BC my senior year in high school. I failed calc 2 freshman year of college, so I'm retaking calc 1 and 2 this year. In high school, related rates were so complicated and stressful, so I was dreading doing them again this year. After watching this video, I had the problem done in maybe 2 minutes. Great video, very clear and helpful. You're doing God's work Dave! :D

[@arthursodsod3232]

I've never been so nervous my whole life about an examination (which is tomorrow). This video will definitely help me pull through. I almost got the question by the end right (forgot to answer with the unit of measurement, but I got the numbers right, which is a feat for me). Hope I'll pass this first year as a college student. Thanks!

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Did you pass?

[@ATorres0821]

You make me actually want to apply related rates in real life. Thank you for keeping the material simple and sensible! 😃

[@livbensen1898]

this video saved my life. I have a test for calc in about 5 hours and i feel much more confident. thank you!

[@topsprout9275]

Why did this one video make more sense than the two weeks we spent on this topic in my AP Calc class?? You might've just saved my test grade tomorrow.

[@CarsonG1017]

My differential calculus final is in 15 minutes. This was the only thing I was struggling with, and its been about a third of the class! Now I think I finally understand it!

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THANK YOU SO MUCH. PLEASE KEEP DOING WHAT YOU'RE DOING!

[@ScratRedemption]

Mathematics has always fascinated me from a statistical standpoint, as certain topics are learned much quicker to some vs others. For example, in my calculus class this most recent fall, my entire class had trouble with related rates but mastered optimization. I was the sole student where that was the opposite; Related rates were easy, optimization was not. When you get to calculus-difficulty in math, there isnt really a "best student", as some people can pick up on topics easier than others, so my advice to those that are struggling is to make lots of contacts in class to find out who picks up on what the fastest, and in case you are that person, to help others in your class.

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nerd

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nerd

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lol, it's nerds like me that made your phones losers

[@bunnygod3948]

You guys are reading the comments on a calculus video and decide to call someone a nerd? I'd think again about that

[@naturerey1845]

I personally find this insanely difficult due to the ambiguity of some of the problems

[@kingsleynnadi9619]

Im a highschool student having calculus trouble but these videos really help alot 😀 Thanks Professor Dave.

[@__lunareclipse]

This is a really great explanation, neat, and much better than my teacher. Thank you!

[@jjdane6227]

Thank you so much Professor Dave, at least now im beginning to see the significance of derivatives and of the course as a whole :)

[@danielvides1741]

Beautiful explanation, the first 5 minutes really helped me conceptualize this topic!!!! Much thanks!!!!!

[@alexh5725]

What really made related rates click for me was realizing what we're differentiating with respect to when we solve a problem. What I mean is that I was used to d/dx, but with a related rate problem, you're differentiating X and Y with respect to time. So rather than dy/dx and dx/dx, it's dy/dt and dx/dt

[@naitaliah3549]

great explanation. I was having so much trouble understanding this and you made it 100x easier! definitely earned my suscribe. thank you!

[@Dusk007]

This video is fantastic. I could not grasp this concept in class but this was simple and easy to understand. Your work is legendary.

[@engineering5]

facts this is better than collegeboard

[@MTLTV-eu4nv]

I at one time had a professor who made fun of the ladder problem. Also, when I was in high school, I took calculus (we used textbooks by same author in both high school and in college), and we talked about how some of the problems in the book are not “realistic.” For example, I cannot think of a reason why you would pull a ladder away from a wall like the situation in this problem.

[@biz_wiz_tech]

simply amazing finally understand related rates ​

[@juancaro3188]

You explain this so well thank you

[@AlexS-vz7od]

What does it mean to have dV or dr or dt just on its own and not in a derivative fraction? Here is what I mean. First example can also be solved like this: dV/dr = 4pi*r^2 --> dV = 4pi*r^2 * dr dV/dt = 100 --> dV = 100*dt 4pi*r^2 * dr = 100*dt dr/dt = 100/(4pi*r^2) etc My question is, what is actually happening when the separate d terms start bouncing around in the expressions? Are they just infinitesimal changes in a variable? It's strange that they can be split off from derivative fractions and recombined to form a different derivative.

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I’m definitely going to be using your Calc vids to help me study for my test tomorrow

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Thanks so much for your help I struggled on problems like this in my college class but I understand how to do them since you explain them so well, thanks you saved my grade

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How simplified and to the point !🔥👍THANK U

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i wish all proffesors could explain like you

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Very good video! Easy to understand, thanks so much!!

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The sliding ladder is my grade in calculus.

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felt

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Perfect best explanations ever, with all the colors X,Y's very easy to follow thanks.

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Maths turns out to be so useful. Thank you for the video!

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Late night study preechhhh

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my midterm is in 15 minutes 🙏

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Very helpful, thanks Prof' D.

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Omg where have you been all my life 👍👍👍👍 ... I like the way you explained things.

[@Historegon]

Sitting on the toilet 20 minutes before my calc final.. let’s hope this helps!

[@md.tanbirulislam]

I learnt new things. Thank you, professor.

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Thank you for this amazing explanation🙌🏼

[@MattyP62]

Thank you so much for this amazing video! God bless!

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i hope that all professors explain like you

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You sir are a legend for this

[@epicwin2513]

i know these aren't necessarily hard, but i just did the practice problem in my head and now i feel amazing

[@nedichaney]

It helps a lot. Thank you!

[@SebastianRocks1234]

OMG thank you so mcuh, I could not get related rates, and all the videos were terrible for it. This made it soo clear omg.

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Sir it's really good explanation , you've solved my big problem...!

[@marc3017]

Im an Electrical Engineering Student, and yeah my finals in differential calculus is in an hour yet im here watching your best videos in order to pass, thanks.

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Very very helpful for my calculus 1 mid exam Thx professor Dave

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Wow....you bring calc to LIFE!

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Thank you so much Professor

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Excellent presentation

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Excellent video. Very clear explanation !

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Typical procrastinator here, thanks for the video! I have a test in an hour and needed this.

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Wow this helped out a lot! Thank you so much

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Great explanation! Thanks!

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This guy is a lifesaver.

[@HardstuckIronAlaynac]

thanks this was really helpful!

[@akashthebot7265]

Dave please give second part of this type of applications of calculas.

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It really help prof. Thanks

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Professor Dave you're saving my life

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i love when you explain

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This was very helpful thank you so much🙏

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thanks for this explanation

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how can someone be that serious after having an introduction like that ... Lol i am laughing 0:03

[@mr_mouli_10]

extrodinary video sir thank u

[@renewd]

This is in regard to differentiating V= 4/3(pi)r^3 On the left side of the equation, didn't you first find d/dV of V which is 1 and then multiply that by dV/dt?

[@AppoIIo]

THANKS I HAVE MY FINAL TOMORROW this totally saved me if theres related rates problems on it

[@esthertesfai9559]

thank you so much! helped me a lot

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Excelente como siempre! :)

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I am in the ninth grade and was interested in calculus but found it too complicated but your videos make it seem so easy tysm

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Thank you

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Wow..I love the ladder explanation

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your videos are amazing

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Appreciate the content!

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very nice! keep it up sir!!!!!

[@Ramkumar-oh8hd]

Best explanation of derivatives

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Fascinating.

[@iibravesii2777]

I'll be honest I failed calculus because of this section of the semester I just couldn't grasp the concept. It clicked when I watched this video, thank you so much.

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Thank you!

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I remember this even though I was horrible at it. Great job. 👍🏽👍🏽

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So helpful!

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Same guy that helped me pass ap bio helping me pass calc now

[@rileygent6225]

My professor contradicts everything he says every 5 seconds and his accent is so thick that he is unable to pronounce the words equation, derivative, and many other mathematical words. I learned more in 2 minutes of this video than the 2 hours of lecture devoted to this.

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I appreciate this

[@Oscar-gx2yf]

Dude, you are awesome

[@EnvisageKenya]

Wow.. can you change the picture in the frame with an implicit differentiation formula?

[@ethana2359]

i visited this topic in Calculus AB 1 year ago and didn't understand it even after watching this and a bunch of videos. for some reason this year in Calculus BC I understand it a lot more. weird how much can change in a year. anyways thanks for the video

[@sanjupradeep9512]

2:31 - In this equation, volume is written as the function of radius. If we plot the graph with V and r , we get a curve. Then the differentiate at any point on the curve will show the slope at that point. Then how can you differentiate the function with respect to time which is neither X or Y coordinate even it is indirectly depended on the function. How can we imagine it.

[@Wutheheooooo]

if i actually understand it true. You can see it seperately as each graph. V(t) and r(t), and we are finding dr/dt using the relation given by the function V(r) and the given information of dV/dt. Just like position, speed and acceleration. we got p(t), s(t) and a(t) as each seperate term

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