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!
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
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.
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!
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.
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.
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
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 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.
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
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!
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 understood related rates my prof is amazing, but i get confused with which number is which 🙃 i really hate related rates but so happy it's just on my exam tomorrow ;-;
10 ft ladder, 6 ft away from wall, sliding 1 ft/s...x will equal 10 ft when the ladder lands, which means it's got 4 ft to go, meaning 4 seconds to slide. If y equals 8, then wouldn't that mean in order for it to go 8 ft in 4 seconds, it would have to be sliding 2 ft/sec on y?
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 learned, but cannot apply in my activity. The teacher gave different problem. *sobbing The examples are relatively easy, but the given problems in the activity aren't. :'))
Me: Maths this complex has no real-world application Dave: What about when you want to calculate the rate at which a ladder is sliding down a wall? Me: 🤨 Er, is everything okay, Dave?
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.
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.
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.
![How to Solve ANY Related Rates Problem [Calc 1]](http://i.ytimg.com/vi/gBHIZlF0TX8/mqdefault.jpg)
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'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.
Yeah I’m cooked
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 video saved my life. I have a test for calc in about 5 hours and i feel much more confident. thank 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
It’s ggs you guys
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
You make me actually want to apply related rates in real life. Thank you for keeping the material simple and sensible! 😃
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?
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.
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!
Thank you sir for your dedication and for making this free! 🙏
The sliding ladder is my grade in calculus.
felt
Late night study preechhhh
simply amazing finally understand related rates
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 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.
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
You explain this so well 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?
Dave please give second part of this type of applications of calculas.
how can someone be that serious after having an introduction like that ... Lol i am laughing 0:03
my midterm is in 15 minutes 🙏
Sitting on the toilet 20 minutes before my calc final.. let’s hope this helps!
midterms is 30 mins away
Wow....you bring calc to LIFE!
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 🤦♂️🤦♂️🤦♂️
Ick-- imperial measurements....SI please!!!
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.
Wow this helped out a lot! Thank you so much
Can you PLEASE DO A VIDEO ON introduction to related rates with TWO EQUATIONS!? In calculus
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.
Appreciate the content!
Thank you so much for this amazing video! God bless!
Wow..I love the ladder explanation
It helps a lot. Thank you!
thanks this was really helpful!
extrodinary video sir thank u
Fascinating.
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?
Thank you sir
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)...
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.
This is a really great explanation, neat, and much better than my teacher. Thank you!
Anyone else with an AP test Monday?
Im a highschool student having calculus trouble but these videos really help alot 😀 Thanks Professor Dave.
i wish all proffesors could explain like you
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 SO MUCH. PLEASE KEEP DOING WHAT YOU'RE DOING!
Excelente como siempre! :)
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!
thank you so much! helped me a lot
this is awesome !!
i think i can finally stop being scared of application of derivatives lol
I regret taking Calculus BC in high school
I cant believe I actually found Math Jesus.
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
Typical procrastinator here, thanks for the video! I have a test in an hour and needed this.
I appreciate this
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.
THANKS I HAVE MY FINAL TOMORROW this totally saved me if theres related rates problems on it
i understood related rates my prof is amazing, but i get confused with which number is which 🙃 i really hate related rates but so happy it's just on my exam tomorrow ;-;
10 ft ladder, 6 ft away from wall, sliding 1 ft/s...x will equal 10 ft when the ladder lands, which means it's got 4 ft to go, meaning 4 seconds to slide. If y equals 8, then wouldn't that mean in order for it to go 8 ft in 4 seconds, it would have to be sliding 2 ft/sec on y?
the rate of change of y will itself be constantly changing! it is accelerating due to gravity.
.
Ah! Gotcha.
You are the best!!!
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
very nice! keep it up sir!!!!!
Love this guy
professor Dave strikes again
ap Calc bc exam gang
Very good video! Easy to understand, thanks so much!!
Repeat the same question by without the ladder length please.
I think this guy is reading out of my calc textbook. The examples he shows are the same as the ones I just tried to read. That's convenient😂
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
my final is in 3 hours
Done.
I learned, but cannot apply in my activity. The teacher gave different problem. *sobbing
The examples are relatively easy, but the given problems in the activity aren't. :'))
Me: Maths this complex has no real-world application
Dave: What about when you want to calculate the rate at which a ladder is sliding down a wall?
Me: 🤨 Er, is everything okay, Dave?
I'm in calc 2 and the shadow problems still get me everytime...
Shadow problems annoying af
Thank you
this video made me feel like im in high school instead of HELL
POV: your final is in an hour so now you’re near tears trying to remember what to do
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.
I’m definitely going to be using your Calc vids to help me study for my test tomorrow
very good
Omg thankyou
My final is in 5 hours, thank you.
Is that a nautilus shell tattoo on your left forearm? Badass if it is 👍
check out "ask professor dave #3" i talk all about it!
great explanation. I was having so much trouble understanding this and you made it 100x easier! definitely earned my suscribe. thank you!
Wow.. can you change the picture in the frame with an implicit differentiation formula?
thank you so much you just saved me
Sir it's really good explanation , you've solved my big problem...!
Whoa, I didn't think I'd get it! My test is in a few hours.
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.
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 finals is 3 minutes away😎
so THAAAAAAAAAAATH'S how you do it!
Beautiful explanation, the first 5 minutes really helped me conceptualize this topic!!!! Much thanks!!!!!
Thats very good profesor dave.i love physics and calculus.your video is very very very Good 😃😃.
Plz make a video on vector calculus.good blasé you.😇😇😇
This explanation for the first phase of the university