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.
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 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!
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.
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.
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!
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
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.
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 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 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!!
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.
@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 💀
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.
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
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.
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
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.
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.
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?
I have a question, if the result is negative, the final answer is negative or positive? some people say its positive because we are talking about how fast, but some people says it's negative.
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
![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...
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 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!
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 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
this video saved my life. I have a test for calc in about 5 hours and i feel much more confident. thank you!
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.
Why'd you get blocked?
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
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!
You make me actually want to apply related rates in real life. Thank you for keeping the material simple and sensible! 😃
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
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
Thank you sir for your dedication and for making this free! 🙏
Im a highschool student having calculus trouble but these videos really help alot 😀 Thanks Professor Dave.
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.
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.
THANK YOU SO MUCH. PLEASE KEEP DOING WHAT YOU'RE DOING!
This is a really great explanation, neat, and much better than my teacher. Thank you!
I’m definitely going to be using your Calc vids to help me study for my test tomorrow
The sliding ladder is my grade in calculus.
felt
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
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 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!!
i wish all proffesors could explain like you
simply amazing finally understand related rates
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.
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’s ggs you guys
Beautiful explanation, the first 5 minutes really helped me conceptualize this topic!!!! Much thanks!!!!!
This guy is a lifesaver.
Thank you so much Professor Dave, at least now im beginning to see the significance of derivatives and of the course as a whole :)
i know these aren't necessarily hard, but i just did the practice problem in my head and now i feel amazing
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.
Very good video! Easy to understand, thanks so much!!
You explain this so well thank you
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
THANKS I HAVE MY FINAL TOMORROW this totally saved me if theres related rates problems on it
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.
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
great explanation. I was having so much trouble understanding this and you made it 100x easier! definitely earned my suscribe. thank you!
i hope that all professors explain like you
Thank you
Typical procrastinator here, thanks for the video! I have a test in an hour and needed this.
How simplified and to the point !🔥👍THANK U
Sir it's really good explanation , you've solved my big problem...!
Wow....you bring calc to LIFE!
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.
Best explanation of derivatives
I learnt new things. Thank you, professor.
Dave please give second part of this type of applications of calculas.
Great explanation!
Thanks!
Excellent video. Very clear explanation !
It really help prof. Thanks
Perfect best explanations ever, with all the colors X,Y's very easy to follow thanks.
Omg where have you been all my life 👍👍👍👍 ... I like the way you explained things.
Maths turns out to be so useful. Thank you for the video!
as someone struggling in college calc 1, I love u
Professor Dave you're saving my life
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.
The only confusing part of this "lecture" was that you used feet in the second example(So it wasn't confusing. You explained it very well)...
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.
i love when you explain
Thank You so much
Very very helpful for my calculus 1 mid exam
Thx professor Dave
Thank you so much Professor
thanks for this explanation
Whoa, I didn't think I'd get it! My test is in a few hours.
Fascinating.
Ick-- imperial measurements....SI please!!!
Very helpful, thanks Prof' D.
Thank you sir
thank you so much you just saved me
how can someone be that serious after having an introduction like that ... Lol i am laughing 0:03
Wow this helped out a lot! Thank you so much
You sir are a legend for this
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.
Great explanation!! Good job !
It helps a lot. Thank you!
Appreciate the content!
Same guy that helped me pass ap bio helping me pass calc now
your videos are amazing
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?
So helpful!
thanks this was really helpful!
Thank you for this amazing explanation🙌🏼
Wow..I love the ladder explanation
I have a question, if the result is negative, the final answer is negative or positive? some people say its positive because we are talking about how fast, but some people says it's negative.
extrodinary video sir thank u
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 🤦♂️🤦♂️🤦♂️
thank you so much!!
midterms is 30 mins away
Thank you so much for this amazing video! God bless!
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
This was very helpful thank you so much🙏
Can you PLEASE DO A VIDEO ON introduction to related rates with TWO EQUATIONS!? In calculus
I remember this even though I was horrible at it. Great job. 👍🏽👍🏽