Directional Derivatives (KristaKingMath)

Подписаться 268 тыс.

Просмотров 143 тыс.

50% 1

► My Partial Derivatives course: www.kristaking...
In this video I explain a directional derivatives calculus problem example.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
● ● ● CONNECT WITH KRISTA ● ● ●
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.kristakingm...
FACEBOOK // / kristakingmath
TWITTER // / kristakingmath
INSTAGRAM // / kristakingmath
PINTEREST // / kristakingmath
GOOGLE+ // plus.google.co...
QUORA // www.quora.com/...

Опубликовано:

16 сен 2024

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 216

@AzoraX0 5 лет назад

SO MUCH BETTER AT explaining than everyone else. Cheers

@redabitar 10 лет назад

Incredibly informative and thorough, a real step by step guide to the experienced and the unexperienced! Awesome work you are doing there. Respect

@kristakingmath 10 лет назад

Wow, thank you so much!

@ssj3vegeta103 9 лет назад

Thank you so much! You might have just saved me on my final.

@dennyyang1630 10 лет назад

2nd day of watching your videos, and I am already impressed by the quality of information, details, and just how knowledgeable you are. This is my final semester of Calculus and It has been a much better experience when I watch your videos. Will be considering to join your Academy soon.

@kristakingmath 10 лет назад

Thank you so much! I'm just glad to hear you're having a better experience with calculus, and I hope the videos will continue to be helpful!

@Captain_Jack514 9 лет назад

I couldn't keep up with anything in class about this. After watching this video, I could do pretty much every problem assigned in the book. You are a life saver.

@kristakingmath 9 лет назад

+C@ptain_Jack That's awesome! I'm glad I could help.

@jakenguyen2584 9 лет назад

i dont always comment on youtube videos but you are really great. My math teacher has a doctorate or something but he can't explain as well as you do. Massive props to you !! Keep it up

@kristakingmath 9 лет назад

Hoang Nguyen Thanks!!

@TheSinghFreestyler 8 лет назад

u r amazing teacher with exceptional skils of teaching to even a student like me who doesnt ask questions in class and ask questions on youtube

@kristakingmath 8 лет назад

+SinghFreestylers - Football entertainment channel Thank you so much!

@ull893 7 лет назад

Awesome. ! I like the fact you explain each and every step, and not assuming that the student knows it. 90 % of the time, students fumble on those steps where the teacher assumes that the student knows, or will not explain because it is too big for his or her ego to explain to small insignificant beings called students. Thank you for the video.

@kristakingmath 7 лет назад

Thanks! I always hated when steps were skipped, so I try not to do the same. :)

@T4BoyRobot 9 лет назад

Thank you so much for your videos! Between you and Sal Khan, engineering school has been almost not brutal.

@TheBigHeinousAnus 10 лет назад

This video and your video on local extrema are extremely helpful. Thank you for making them!

@kristakingmath 10 лет назад

You're welcome, I'm glad they helped!

@mehularora1813 3 года назад

I genuinely wish this channel had more subscribers... Thanks for these amazing videos, Krista!

@kristakingmath 3 года назад

You're welcome, Mehul, I'm so glad you're enjoying the videos! :)

@iflashlantern4292 4 года назад

It's been over 9 years and she still likes and responds to comments. That's epic.

@kristakingmath 3 года назад

That's sweet of you, Robert! I do my best to get back to as many people as I can! :)

@humphreyatanglekhoba2470 8 лет назад

This is very clear and easy to understand. Thank you Krista

@kristakingmath 8 лет назад

+Atang Lekhoba You're welcome, I'm so glad it made sense!

@hpdixon1 11 лет назад

a directional derivative evaluates the instantaneous rate of change at a given point in the specified direction (of the direction that has been chosen). So, directional derivatives are mostly used to describe rate of change for functions with multiple variables (like 3-dimensional spaces).

@garyadamos 4 года назад

Thank you so much you are the only youtube channel that has been helping me answer my homeork. Love from UCSD!!

@peterh.1521 8 лет назад

Simply excellent! Very clear instructed Krista of the directional derivative! Impossible to outdo. :)

@kristakingmath 8 лет назад

+peter hansi Thank you so much, Peter!

@atillathehun6434 3 года назад

Wow, simply explained with focus in practical application. Thank you!!

@kristakingmath 3 года назад

You're welcome, I'm so glad you enjoyed it! :D

@patrickdoll6036 8 лет назад

This videos are helping me get through Calc 3 hahaha so much better than lecture. You're the best Krista!

@kristakingmath 8 лет назад

Yay! I'm so glad the videos are helping. :)

@chihaya1119 8 лет назад

Super helpful, can't pass my exam without using these video

@kristakingmath 8 лет назад

I'm so glad it helped!

@gravewalker_0125 8 лет назад

Thank you very much I have had trouble with some of these concepts but you have made it so easy to learn and understand. You are the best!

@kristakingmath 8 лет назад

Thank you so much, I'm so glad this helped!! :D

@JackLe1127 9 лет назад

i've been searching for hours and there isnt a video that explains the purpose of directional derivatives yet. when i learn something i need to know why and when to use it

@T4BoyRobot 9 лет назад

It's the multivariable version of the slope of a curve. It has a lot of uses. The obvious one, for instance, is it can tell you the steepness of any three dimensional surface at a given point in any direction. It's also intertwined with the gradient (the vector pointing towards the steepest slope away from a given point), which is immensely important for optimizing just about anything. This guy has a great description: betterexplained.com/articles/vector-calculus-understanding-the-gradient/

@TrinoElrich 8 лет назад

+Jack Le might be a lil late to the party, but in all honesty, it looks to me like the directional derivative is a generalization of the partial derivative in the sense where you can take partial derivatives outside of simply making your multivariable function change specifically with respect to only one of the two axes (x- and y-axes).

@MrMirroru 6 лет назад

wow, so clear and organized, Thanks, Krista!!

@kristakingmath 6 лет назад

You're welcome, I'm so glad you liked it. :)

@fayyazakhthershareef 9 месяцев назад

My math is soooooooooo week😢but you are amazing teacher ❤ but only you're videos understand❤❤❤

@kristakingmath 12 лет назад

Absolutely. Your vector could be (1)i+(1)j, instead of v=(1,1), if you wanted it to be. :)

@vanillapie8321 3 года назад

so much better than my zoom college classes! Please be my professor.

@Seant885 9 лет назад

Thank you so much! You are great at clarity and conciseness.

@kristakingmath 12 лет назад

Right back at ya! Thanks for the comment. :)

@rockyshepheard6054 6 лет назад

Thanks. Easy to understand. You might want to mention that you dot producted the unit vector with the partial derivatives though. Although you did it, you didn’t state it explicitly.

@samu4890 8 лет назад

Thanks so much for these video. I honestly wouldn't know what to do without these. Do you ever take request?

@kristakingmath 8 лет назад

I'm so glad you like them! I don't specifically take requests, but please let me know what you'd like to see more of so that I can factor it into my video list!

@kanyisantombini8793 9 лет назад

This is awesome!!!! I am officially addicted to your videos!

@kristakingmath 9 лет назад

Kanyisa Ntombini Yes! Awesome!!

@bigbrendo69 10 лет назад

got my mid sems for this tomorrow, cheers for the help

@kristakingmath 10 лет назад

Good luck tomorrow!

@juniorjay001 5 лет назад

thank you Krista

@randomguy9580 5 лет назад

Thanks you so much, I finally understand! So well explained!

@TanPham-sn3fc 4 года назад

She's so natural!

@Blackfire264 10 лет назад

The helpfulness of this video is too much to handle! One question though: When you are given the direction vector, is it okay to immediately assume that it is NOT in unit vector notation? My textbook uses "arrow" notation (as in a small arrow above the u to denote it as a vector) and the "hat" notation seemingly interchangeably. Because I've grown accustomed to using hat notation for unit vectors and arrows for normal vectors, I'm never sure when I need to change the vector to a unit vector or know if it is already in unit vector notation.

@Emc4421 7 лет назад

Great Vid. Simple and Very helpful. Thanks!

@shubhamkashyap9279 4 года назад

I'm a high school student. This seems interesting. Really it's interesting.. Wanna go through all of your videos in 2 days Or more..

@downloadingutubes 4 года назад

good luck doin multivariable volume calculations and line integrals through vector fields will take u more than 2 days

@vivekvedpathak73 8 лет назад

finally got it!!!..thank u so much krista.

@kristakingmath 8 лет назад

+VIVEK VEDPATHAK You're welcome, I'm so glad it helped!

@kristakingmath 11 лет назад

Glad I could help! :)

@alixaprodev 5 лет назад

thank you. you help me most. i will always watch your videos.

@abdul9525 9 лет назад

Very neat job. Thank you very much. You are very helpful.

@prateekkumar.1325 4 года назад

It is so much easy 2 understand ty so much sis!loved it!

@kristakingmath 4 года назад

You're so welcome, Prateek, I'm so glad it made sense!

@shaimaasadoun4797 5 лет назад

I do not know how to thank you u saved me tomorrow I have an exam Thank you from the bottom of my heart 🥰😘😍😍❤️❤️❤️ Shaima from the State of Iraq🇮🇶🇮🇶🇮🇶

@kristakingmath 5 лет назад

I hope the exam went great! :D

@nathangillespie9704 6 лет назад

Super helpful, everything makes sense now. Thank you so much!

@jeffersonumara2371 4 года назад

You made it look super easy

@omarshokry7022 8 лет назад

this is so amazing. Thank you Krista king ^_^

@kristakingmath 8 лет назад

You're welcome, I'm glad you liked it!

@TheL4ets 11 лет назад

These videos are great! I should have found them earlier! My exam is in 8 hours, and my 'foundations' are still shaky... We'll see how that ends.

@spellcheek 9 лет назад

you are doing the lord's work.

@dhimanroy1671 8 лет назад

Thanks for your very good teaching

@kristakingmath 8 лет назад

+Dhiman Roy Glad you like it!

@ArslanAli-cs1be 7 лет назад

Your voice is very soothing and lovely as your tutorials are efficient plus i think i am in love with you r tutorials :o

@ut2usr2 11 лет назад

Smart. But, faster to simplify before replacing x and y values. (1/sqr(2)) (4x+8y) = sqr(2) 8. Great job.

@kristakingmath 12 лет назад

@Jirethify So glad I could help! :)

@kristakingmath 12 лет назад

You're welcome! :)

@MsAmiSay 12 лет назад

This video made so much sense! Thank you for being so clear and helpful. But I was stuck on doing these types of problems where you are solving for the partials of fractions such as x + y / y+1, seems simple but I am sooo lost cause we have to solve for the gradient. Is there any way you should show how to do a problem like that?

@kristakingmath 12 лет назад

You're very welcome!! :D

@emranmalik_007 Месяц назад

best explanation , TYSM and I just subscribed :)

@kristakingmath 12 лет назад

@Waqasgju You're welcome!! :D

@JiyaadTahir 9 лет назад

what if there is a fraction attached to the vector? so v = 1/3 Do you just expand the bracket and then square root a+b+c?

@barulli87 10 лет назад

great explanation, but i still have one doubt, sometimes the point used to find the unit vector is X-X0 and not X, could you explain this please?

@karabotshehla3967 6 лет назад

Thank you so much you really are a king

@CelestaleOfficial 10 лет назад

Nice tutorial video! What if the question doesnt gives me a direction vector? I'm only given a function z=z(x,y)=xye^x and a Point( 1/sqrt2, 1/sqrt2). Could you explain this please?

@tampaflorida33610 9 лет назад

keep up the good work, u r awesome and i am sure u will have bright future

@kristakingmath 9 лет назад

thank you very much!

@katek5568 7 лет назад

how are you so clever? thank you so much Krista. I feel clever after watching this😂😂😂

@kristakingmath 7 лет назад

I'm not sure if it's clever, as much as it is just a lot of practice, lol. :D

@kristakingmath 7 лет назад

This is everything I use to make the videos: www.kristakingmath.com/blog/how-i-create-my-videos :)

@mohammadalnasser6587 10 лет назад

Thank you very much, you helped me to understand this problem even more. :)

@kristakingmath 10 лет назад

That's great! You're welcome. :)

@seven-mod 7 лет назад

I LOVEEEEE YOUUUUUUUUUUU my savior

@anoniem012 5 лет назад

Thanks! This did solve my problem.

@kristakingmath 5 лет назад

Oh good! So glad it helped! :D

@evrarddarenberg8311 10 лет назад

One thing is really bad here, is that you dont explain that the length of your vector has to be = to 1 -> Pythagore. The rest was pretty good and clear

@kristakingmath 12 лет назад

Awesome, you're welcome! :)

@ronnies.3440 7 лет назад

Thank you for your helpful videos!

@kristakingmath 7 лет назад

Glad they're helping!

@kristakingmath 11 лет назад

I hope it went well! :)

@MrJPawelHeaven 11 лет назад

hello, I have a question - In this example whe had a vector v and we wanted to find a directional derivative at point P. My qustion is related to a gradient. Because we had in this example a given vector v, does it mean that our computed directional derivative may not point to the highest point on a plane?

@jacobvandijk6525 3 года назад

Sorry, but I totally miss the intuition behind this concept. With (for example) df/dx = 3 I know that dx = 0,001 will give me df = 0,003. But I have no idea what the Dir.Der. does to df after some marginal change?

@Christiskingofkingslordoflords 9 лет назад

Thank you very much. Great work!

@kristakingmath 9 лет назад

Thanks!

@chrisskahill853 8 лет назад

are you always given a vector and a point?

@joseroman158 6 лет назад

thanks! you helped me out a lot!

@TheSarahdacosta 7 лет назад

Thank you so much! Such great help, really appreciate it!

@kristakingmath 7 лет назад

So glad I could help Sarah! :)

@zahrashaker9913 8 лет назад

Super helpful, Thank You so much.

@kristakingmath 8 лет назад

You're welcome, I'm glad it helped! :)

@LeandroMayor 11 лет назад

Thanks so much, it was very helpful

@SAYYAM55 10 лет назад

Thanks a lot, this is really helpful !

@kristakingmath 10 лет назад

Glad I could help! :)

@jonescyril8042 Год назад

LOVED IT

@TimTim-tz2yt 6 лет назад

Awesome I just understood this

@mrinmayeebangar7207 7 лет назад

thank you so much what to do when directional vectors are not given??

@kristakingmath 11 лет назад

Love you too! :)

@edrysha4654 8 лет назад

Thank You very2 much. This video help me a lot.

@kristakingmath 8 лет назад

+edry sha You're welcome, I'm so glad it helped!

@joem6065 6 лет назад

easily understood thank you.

@kristakingmath 6 лет назад

You're welcome, I'm so glad it helped!

@felidiazr 10 лет назад

thanks for your explanation, greetings from chile :)

@kristakingmath 10 лет назад

Glad you liked it! :)

@tahermahmud3053 Год назад

Thank youu !! from Bangladesh

@shensley011 6 лет назад

Why am I seeing in some of my problem sets gradient of f dotted with unit vector? Does this formula also give us the directional derivative or is this something different?

@jennymwamba3116 5 лет назад

Thank you 😊

@MyAmazing91 9 лет назад

A million thanks :)

@elmo1702 10 лет назад

This was really helpful, thank you so much :)

@kristakingmath 10 лет назад

i'm so glad it helped!

@mireazma 7 лет назад

Krista, for goodness sake where did you get that cursor?

@Wamaroa 6 месяцев назад

Thank you...❤

@kristakingmath 6 месяцев назад

You're welcome! 😊

@saif8485 4 года назад

well explained thank you

@kristakingmath 4 года назад

Thanks, Saif! :)

@fouadhaidar3640 8 лет назад

If we need to find the unit vector in the direction of which the maximum rate of change occurs, we use (df/dx,df/dy) as (a,b) then we use the formula to get the answer? Is that correct?

@frehunassefa2850 8 лет назад

If we need to find the unit vector in the direction of which the maximum rate of change occurs, we use (df/dx,df/dy) as (a,b) then we use the formula to get the answer? Is that correct? woul you please answer this question! THANK YOU VERY MACH AS ALWAYS.