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.
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!
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)
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.
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!
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
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.
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!
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.
Bro my teacher just did these problems with no explanation and ive been lost for a month, my quiz is today and i was screwed but this makes SO MUCH MORE SENSE. Thank you for explaining WHY you were doing something rather than just adding derivatives.
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.
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.
I couldn't do a single related rates problem until this video and I did the practice al by myself! Thank you so much professor dave!! Every time your theme song comes on I do a dance!!
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
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.
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.
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.
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
@polygondeath2361 in all seriousness, this isn't too hard. But it's easy to mess up with derivatives in general when you've got sloppy algebra skills, lol. Wish me luck brø, my exam's tomorrow 💀
he's differentiating with respect to t, so implicit differentiation is being used here [which gets us 2x(dx/dt)] instead of just normally finding the derivative of x^2 (2x). basically we have to do this since we know dx/dt and must incorporate it into the formula to find dy/dt. hopefully that makes sense.
![How to Solve ANY Related Rates Problem [Calc 1]](http://i.ytimg.com/vi/gBHIZlF0TX8/mqdefault.jpg)
I'm a college student, this is one of the best math explanations videos I've seen in my life. Great Job
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.
My final is in an hour
Same. Time is ticking
Jossiah Siapno my time to shine
Lol same
This makes me feel better. My test on derivatives is in 17 hours.
Well, fuck... I'm in the same situation currently... My final is in 24 hours from now...
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!
This is probably the only channel where one can want to continue learning new concepts. Waiting for the next.
that's the best kind of compliment! thanks kindly!
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)
How was your ap calc??
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.
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!
Did you pass?
i wish all proffesors could explain like you
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
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.
this video saved my life. I have a test for calc in about 5 hours and i feel much more confident. thank you!
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.
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!
This video is fantastic. I could not grasp this concept in class but this was simple and easy to understand. Your work is legendary.
facts this is better than collegeboard
Magnificent explanation of the concept, recommended if you have a final in an hour.
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.
nerd
nerd
lol, it's nerds like me that made your phones losers
You guys are reading the comments on a calculus video and decide to call someone a nerd? I'd think again about that
I personally find this insanely difficult due to the ambiguity of some of the problems
I love that this series has a blues clues vibe but also one of the best on youtube for learning.
Im a highschool student having calculus trouble but these videos really help alot 😀 Thanks Professor Dave.
Thank you sir for your dedication and for making this free! 🙏
professor dave still saving lives in 2025
You make me actually want to apply related rates in real life. Thank you for keeping the material simple and sensible! 😃
This is a really great explanation, neat, and much better than my teacher. Thank you!
Bro my teacher just did these problems with no explanation and ive been lost for a month, my quiz is today and i was screwed but this makes SO MUCH MORE SENSE. Thank you for explaining WHY you were doing something rather than just adding derivatives.
THANK YOU SO MUCH. PLEASE KEEP DOING WHAT YOU'RE DOING!
This guy is a lifesaver.
I’m definitely going to be using your Calc vids to help me study for my test tomorrow
how can someone be that serious after having an introduction like that ... Lol i am laughing 0:03
simply amazing finally understand related rates
The sliding ladder is my grade in calculus.
felt
Typical procrastinator here, thanks for the video! I have a test in an hour and needed this.
Wow....you bring calc to LIFE!
It’s ggs you guys
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.
Professor Dave you're saving my life
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.
Beautiful explanation, the first 5 minutes really helped me conceptualize this topic!!!! Much thanks!!!!!
I couldn't do a single related rates problem until this video and I did the practice al by myself! Thank you so much professor dave!! Every time your theme song comes on I do a dance!!
Maths turns out to be so useful. Thank you for the video!
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
THANKS I HAVE MY FINAL TOMORROW this totally saved me if theres related rates problems on it
Thank you so much Professor Dave, at least now im beginning to see the significance of derivatives and of the course as a whole :)
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
Omg where have you been all my life 👍👍👍👍 ... I like the way you explained things.
great explanation. I was having so much trouble understanding this and you made it 100x easier! definitely earned my suscribe. thank you!
Very good video! Easy to understand, thanks so much!!
Bro this channel is actually S teir.
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.
Sir it's really good explanation , you've solved my big problem...!
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.
You explain this so well thank you
I learnt new things. Thank you, professor.
i hope that all professors explain like you
Best explanation of derivatives
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.
Great explanation!
Thanks!
My whole night is summarized in 8 mins. Should have watched this a lil bit earlier
Our midterms is 3 hours from now and here I am just started reviewing 😅
i know these aren't necessarily hard, but i just did the practice problem in my head and now i feel amazing
Wow,this is a gorgeous explaination.
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
It's midnight and I have an exam tomorrow
Good ppl still exist , thank u professor
same my exam is tmrw but i’m not gonna do well i have no idea how to do anything in calc
@@nn-lh8he Same. I only know derivatives, but they're easy. My professor sucks too.
Sitting on the toilet 20 minutes before my calc final.. let’s hope this helps!
How simplified and to the point !🔥👍THANK U
your videos are amazing
thank you so much you just saved me
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.
Whoa, I didn't think I'd get it! My test is in a few hours.
You sir are a legend for this
Dave please give second part of this type of applications of calculas.
Yeah I’m cooked
Yup
You wouldn't be the only one lol
@@milowskiii5882 worry not I passed the exam and was closer to the top of the class than expected
@polygondeath2361 in all seriousness, this isn't too hard. But it's easy to mess up with derivatives in general when you've got sloppy algebra skills, lol.
Wish me luck brø, my exam's tomorrow 💀
@@milowskiii5882 honestly having a strong algebra foundation is critical to doing well in calculus. I wish my earlier math classes were thus better
It really help prof. Thanks
Perfect best explanations ever, with all the colors X,Y's very easy to follow thanks.
Excellent video. Very clear explanation !
I understand it now
I remember this even though I was horrible at it. Great job. 👍🏽👍🏽
i love when you explain
Late night study preechhhh
Preachhhh
My teacher was kind and let me finish my test next class. I finished one problem in an entire hour 😢 I better not disappoint tomorrow 🤦♂️🤦♂️🤦♂️
as someone struggling in college calc 1, I love u
Appreciate the content!
My midterm is in 3 hours
Feel u bro😂🙏
Wow this helped out a lot! Thank you so much
this is awesome !!
i think i can finally stop being scared of application of derivatives lol
Very very helpful for my calculus 1 mid exam
Thx professor Dave
Great explanation!! Good job !
This was very helpful thank you so much🙏
Better than my calculus teacher
thanks for this explanation
Wow..I love the ladder explanation
Very helpful, thanks Prof' D.
Fascinating.
extrodinary video sir thank u
Thank you so much Professor
So helpful!
Ick-- imperial measurements....SI please!!!
Thank you for this amazing explanation🙌🏼
It helps a lot. Thank you!
Excellent presentation
what is the difference when differentiating x^2,
when is the answer 2x and 2x(dx/dt).
he's differentiating with respect to t, so implicit differentiation is being used here [which gets us 2x(dx/dt)] instead of just normally finding the derivative of x^2 (2x). basically we have to do this since we know dx/dt and must incorporate it into the formula to find dy/dt. hopefully that makes sense.
professor Dave strikes again