Related Rates (KristaKingMath)
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- เผยแพร่เมื่อ 19 มิ.ย. 2024
- ► My Applications of Derivatives course: www.kristakingmath.com/applic...
Understand one of the trickiest applications of derivatives and implicit differentiation, related rates.
Review the spherical balloon and leaning ladder examples to get a better grasp on related rates.
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If you could use some extra help with your math class, then check out Krista’s website // www.kristakingmath.com
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
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Related Rates starts @ 3:19
God bLESS YOU BRO
Personally, I'd never skip Krista.
please do not encourage people to skip in such videos
THANK YOU
thank you!
The sphere and ladder is easy....The one that's gonna be on my test will probably be something like a man is walking from a streetlight and the tip of his shadow is moving.. (aka: 2 right triangles). Thanks for the help though.
I am not going to lie, these videos are getting me through college
OH MY GOD! Why don't they just teach it this way?!?! I've spent a week trying to understand how my course teaches related rates. My online homework "show me an example" section gives me 20+ steps for figuring out the problem and even then I can't consistently get the right answer. This video helped me totally understand related rates in about 9 minutes.
this was the only thing I wasnt clear on, thanks a lot. Now my computer science final is the only one i fail and not calc!! lol
Waffleman60 lol, awesome!!
+Waffleman60 lmao shame
Same
agreed
Watching your videos while doing last minute studying, is so helpful. Thank you! ☺️☺️
"awesome" is the first word that came to mind after watching this video. I now have confidence!! Love you so much.
I have been pouring over related rates, been in tutoring sooooo many hours spent there. This video makes it so easy to understand.
Your videos are the most helpful ones I've seen. I really appreciate the help you give everyone. You are helping me continue with my streak of A's in math.
This is amazing! You are by far the best "related rates" teacher I could find!
Jacob Richman Thank you so much!
Thank you so much for the upload, you speak very clear and the initial steps you gave helped me out a lot thanks
This is a great explanation.
Although most of us understand implicit differentiation, it's only after watching this video that I understood how it is important for related rates.
Q
This seems wrong... How did she get 217pi . When you multiply the values it does not add up!
I know ahah. It should be 10/225pi
It's a mistake. dr/dt = 10/225π in this case.
No wonder I was struggling... my professor completely skipped implicit differentiation and jumped right into related rates :( Thank goodness for this video.
if i m not wrong the denominator answer in balloon problem should be 225pi not 217
Naeem Hakimi ...That is correct and, after further simplification, the answer will be: dr/dt = 2/45pi cm^3/min =
Scott Magnuson It would actually be in cm/min units. As it is the radius's rate that is changing.
So glad they're helping!
Energy - Universe - SCIENCE - I am happy with your LESSON, PLEASE NEVER STOP WITH THIS LESSONS. I AM VERY GLAD, I LOVE TH-cam. I LOVE THE LIFE.
Great video, soothing voice, awesome combination.
I'm already working on it, pretty pumped!! :D
I've never heard it explained clearer (: Thank you so much!
Thanks so much! This helped a lot!
your videos are saving my life. Thank you so much.
Yes, but then in order to get all of the x's on one side and all the y's on another, you'd have to try to divide both sides either by e^x or by e^y. Either way, you'd end up with terms on the left that include both x and y, which you wouldn't be able to separate.
This video is a lifesaver. I was sick for a week when my teacher taught this and I have an exam in a couple of hours. Thank you!
You're welcome, I hope your exam went great!!
3/4 on the exams. Havent got the time to answer the last number. Thank you!
Oh my goodness Krista! You explain this SO much better than my professor 🤗❤
I've been struggling with related rates. This video helped me finally get it. For whatever reason I missed how implicit differentiation was involved. It's so much clearer now. Damn, it's just like how definite integrals are used to find the area between two curves!
Explaining the relationship to implicit differentiation really helped me - thanks!
I have a quiz today over Related Rates and I was kindaaaa freaking out, haha. This helped tons! The examples went at a perfect pace so that I could follow them. You're awesome at explaining the process. ^_^ THANK YOU!
Omg ! I can clearly understand this now and I know exactly why I'm doing it. You've made my life so much easier, thanks a lot !
So glad it could help! 😀
I did well on the exam cause one question was the leaning ladder.
Thank you so much, i will pass calculus because of you !!!
That's always the best feeling! Way to go for sticking with it! :D
Thank you very much for a great video! Perfect for a little repetition before the exam tomorrow :)
Thank you so much!! You are way better than my math teacher :) I will actually do good on my test!
You're so welcome! I hope it goes well for you! :)
Thank you soooo much!!! Got exam next week, so Im gonna watch all your videos. Hahaha!
I'm so glad it helped!! :D
You make clear and precise videos! Thank you very much!
You're welcome, I'm so glad you like them!
that's awesome! good for you for doing so well!! keep it going!! :D
10 years after OP, you have explained better in 2mins what my college professor "taught" us in 2hrs. I cannot thank you enough for these videos.
Both my book and my teacher state that this is done by applying the Chain Rule. I couldn't figure that out because it looked like implicit differentiation to me. Thank you for clarifying and teaching it this way!
+Jason Hall Implicit differentiation is an application of the Chain Rule :)
You are so calm and helpful, God bless you.
+Saron Giday Thank you so much!
I have my calculus exam in an hour and I'm going through all your videos related to my syllabus. And it's making me more confident that i'll do good. Thanks :)
I hope your exam went well!
Very well explained!!
Awesome!!! So glad I could help. :D
Hopefully you'll find them helpful! :) Is your classing coming up this semester?
Thank YOU!! you helped me a lot! was about to write a Calculus test and the night before i saw this video.. helped me a lot in the test
i'm so glad it helped!!
Thank you so much for this video. I have my calc quarterly today and you probably saved me.
Good luck today!
thanks for all you do!!! youre a life saver!!!
I subscribed right after the end of the video. I couldn’t believe I learned more in 8 minutes of this video than I’ve done the past 3 lectures.
Glad it could help! Thank you for subscribing. :)
Awesome explanation! THANK YOU!
Aww thanks! :D
In school today, I lost all hope of understanding related rates....but now i actually understand it, thank you so much!!!!
Awesome! So glad I could help! :)
thank you for explaining it slowly and clearly!
+Armani Araujo You're welcome, I'm glad I could help!
Kris, you are the boss!
the units are cm/min. on the left-hand side, you have 10 cm^3/min, which you can write as (10cm^3)/min. on the right-hand side, you have (7.5cm)^2, so you get cm^2, and when you divide the left-hand side by everything on the right-hand side except dr/dt, you get (cm^3)/(cm^2 min), which leaves you with cm/min. :)
So glad it was able to help! Good luck on your quiz! :)
yea you will be getting my thank yous throughout the semester, you break it down very thoroughly. Thank for investing your time in helping others.
It's my pleasure! I hope the videos will continue to be helpful as you go through the rest of your class!
this helps a lot!
Aw, thanks so much! I need all of that I can get, haha. I think I did pretty well... even figured out some of the extra credit problems. :D Thanks for taking the time & effort to make these videos; they really do help people!!!
PERFECT PERFECT PERFECT PERFECT PERFECT!!! :D Thank you so much! I understand related rates because of this video!! :) (I looked at 2 other videos and was still a little confused) Thank you!
you're welcome! i'm so glad it's helpful. :)
what are the formula u need to know. for the geometry trig and and that stuff
Your videos are very helpful... i actually understand this material now!!!!
I'm so glad it makes sense and that the videos are helping!
I hope it helps! Check out some of the other related rates videos too! Maybe you can start the video to get the problem, then pause it and try to work it on your own, and the play the rest to see if you got it right. :)
Thanks, Teacher. I think you just bought me a few points on the free response for the AP Calc BC exam coming up here. This video clears up so much for me. Realizing that everything has a respect to time(t) simplifies life while still making sense at the same time. Now, to find a video on Maclaurin error bounds ;-;
***** This might help! th-cam.com/video/93-zn9jY-78/w-d-xo.html Good luck on your AP test!!
Thank you! This was super helpful!
You're welcome, Collin, so glad it helped! :)
ive been stuck on this for days.. thank you so much for your detailed explanations!! my calculus teacher has a heavy accent and is a little difficult to understand. Now on to maxima and minima!
+mike genova You're welcome, I'm so glad it helped!
Awesome! An 8 minute video made what seemed like an overall complicated process into a breeze!
+jay212851 I'm so glad it helped!
Do you have any tips for finding the equation? for some reason I have the most trouble with that.
this video saved my life
+Tix Tic You're welcome, I'm so glad it helped!
good god i love these videos
what are the units that the 10/225pi should be in? cm^3/minute?
This video has helped me more than my textbook. Thanks!
You're welcome, I'm so glad it helped!
You're so welcome! That's so nice of you to say. :)
Finally, someone who explained it clearly. Thank you!
:D
Awesome! Glad I could help! :)
although you explained it every well, the first example is actually separable into x and y. Understand that e^(x+y) is actually (e^x)(e^y), move the 3e^y to the right side, factor out the e^y to give: 2x = e^y(e^x-3), divide both sides by the e^x - 3 and we have separated x and y. If you want to see y cleanly all by itself, then take the natural log of both sides: y = ln( 2x / (e^x - 3) ).
However, this problem is definitely much easier to solve using implicit differentiation. I just want to point out that the equation is indeed separable for those who may question it
My new beautiful and intelligent teacher. Thank you so much fam.
Fantastic. A lot of help
I have a calculus paper on Thursday, and you madam, teach 100 times better than my lecturer at campus. I just wish you taught even more stuff like computer programming.
I'm so glad I can help! Good luck on your upcoming test!
Thanks for the valuable informations
awesome
I'm so glad! :D
id ont know if im missing something, but i can't seem to figure out part of your calculation
at 6:00 of the video
10 = 4(π)(7.5)^2 (dr/dt)
you end up with (dr/dt) = 10/(217 π )
but 4 * (7.5)^2 = 225
am i missing something?
Lol, good for you!! It's awesome that you're able to help him! Keep up the good work!! :D
Probably the cutest calculus teacher I've ever seen
this was really helpful for me thank you!
Awesome! Thanks for letting me know. :)
muchas gracias profesora Kiiiing!
Thank you!! :)
these videos are helping so much for my AP test!!!!!! Thank you
you're welcome! good luck on the test!!
thanks so much!!
you're so pleasant, I've been watching your videos for like 30 min and I'm not even taking math this quarter
This was great, should help with the upcoming test. Thanks a lot :)
Lachlan Jones I hope so! Good luck on the upcoming test!
NICE!! Extra credit is the BEST! Way to rock it!! :D
This plus what I learned in class makes things less foggy. Thank you!
+tyrenebanks72 You're welcome, I'm glad it helped!
At 5:59 in the video, you have dr/dt = 10/(4pi*(7.5)^2) to get dr/dt alone. The answer shown is 10/217pi, but I get 10/225pi. 7.5 squared is 56.25, and 56.25*4 = 225. Am I missing something?
No you're right. There was an annotation at 5:48 correcting the error. Sorry about that!
The thing to remember is that pi is a constant (3.14...) 4/3 is also a constant, and when you multiply 4/3 by pi, you still have a constant. Since the whole 4pi/3 value is a constant coefficient on the r^3, you would take the derivative of the whole thing in the same way you'd take the derivative of 5r^3, that is, you'd use power rule. I hope that helps! :)
Thank you!! :D
Question: couldn't you separate the X and Y on the left side by doing e^x(e^y) because of the laws of exponents?
You seriously just saved me days of stress. Thank you so so much.
mchowderz You're welcome, I'm glad it helped!
So find the area formula of the diagram given in the question and then solve for the derivative of that area formula?