Directional Derivatives | What's the slope in any direction?

A directional derivative gives the slope in any particular direction, similar to partial derivatives which give the slope just in the x or y directions. We formally define directional derivatives by modifying the familiar limit definition of the derivative for when you move along some vector in the input space. Then we see a very nice feature that we can use the gradient vector grad(f) to make computing directional derivatives easy. If you have the gradient, you can get the directional derivative in the u direction with one easy dot product.
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Пікірлер: 351

  • @subse5371
    @subse53713 жыл бұрын

    I'm an undergrad and believe me this is the first time i understood anything about calculus hats off man👍

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    @kafuu1

    9 ай бұрын

    thats the power of Internet

  • @mikzin630

    @mikzin630

    8 ай бұрын

    you made it to calc 3 without ever understanding anything about calculus?

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    @shivangsingh5834

    5 ай бұрын

    ​@@mikzin630😂😂

  • @broqentoys
    @broqentoys4 жыл бұрын

    self-studying this over the summer.... wish u were my teacher!! thank you

  • @gonderage

    @gonderage

    4 жыл бұрын

    Yo, me too!

  • @HorizonSpeed26

    @HorizonSpeed26

    3 жыл бұрын

    doing it over winter. Yes, I am a bit mental.

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    @shadabansari9121

    3 жыл бұрын

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    @shadabansari9121

    3 жыл бұрын

    @SHADAB ANSARI , u 2 :)

  • @mosalethoba5267

    @mosalethoba5267

    3 жыл бұрын

    He's your teacher thanks to the internet

  • @jaydean5243
    @jaydean52433 жыл бұрын

    Dr Bazett, your videos are incredible , concise , animated, and to the point, VERY well done. I'm a retired pharmacist , in my spare time i try to keep learning advanced math. were I left off with adv calculus , and ODE (1974) . I appreciate all your time and effort THANK YOU....Jay

  • @chetanraina5649
    @chetanraina56494 жыл бұрын

    This is the best explanation of directional derivatives. Please never delete these videos.

  • @v-doc5230
    @v-doc52303 жыл бұрын

    I am a very experienced engineer, studied mathematics in five different lectures, not including mathematic heavy lectures like aerodynamics, gas dynamics, etc. Yet, I never saw it that way. Very well done and informative! Thanks!

  • @samyakgupta4301
    @samyakgupta43013 жыл бұрын

    Didn't knew that PewDiePie was such a great teacher. Okay sorry. You are awesome Dr. Bazett.

  • @dushyantsengar9381
    @dushyantsengar93814 жыл бұрын

    Amazing animation at start to show directional derivatives. I have really got a better understanding to how to visualize the directional derivative now. Amazing video..keep up the good work :)

  • @pultural
    @pultural3 жыл бұрын

    This video was like the last brick in the wall of understanding gradient and partial derivative, that's insane..I get my 'ahaaaa' moment so fast! Thank you so much, also for explaining how we came from limit to composition function and after applying the chain rule to dot product of gradient vector in the point and unit vector!

  • @muhammadharoonlatif5154
    @muhammadharoonlatif51543 жыл бұрын

    Some of the videos I just watched them because they were so engaging, despite not being part of my syllabus.

  • @effizienzlizenz
    @effizienzlizenz4 жыл бұрын

    I love your enthusiasm. Calculus is beautiful once one has grasped the logic behind algebraic framing of questions.

  • @AndyOrtiz93
    @AndyOrtiz937 күн бұрын

    This video is INSANE. Learned more from this than a 2-hour lecture from my professor 😭

  • @user-jc2uv4re8h

    @user-jc2uv4re8h

    7 күн бұрын

    I don't know why school doesn't teach this way. They only give a bundle of complex formulas without comprehensive explanations and then assign a ton of tedious homework. Thanks to this 12-minute video and a bit of imagination, I can handle all of it.

  • @Hinchey613
    @Hinchey61317 күн бұрын

    The visual explanation up to 2:40 really helped me understand the main concept better.

  • @DrTrefor

    @DrTrefor

    14 күн бұрын

    Glad it helped!

  • @donlansdonlans3363
    @donlansdonlans33634 жыл бұрын

    Omg finally I understand this

  • @MinhLe-se6bs
    @MinhLe-se6bs3 ай бұрын

    Thanks for your explanation. Please never delete this video. You inspire students who want to see the beauty of math. Thanks again.

  • @rockyjoe3817
    @rockyjoe3817 Жыл бұрын

    I am so happy to see your channel getting the recognition it deserves . You really saved me during university period.

  • @darkphoenix_007
    @darkphoenix_007 Жыл бұрын

    Amazing Dr.Trefor.. Never imagined the concepts in this way. Please continue making videos. Big fan

  • @arthurbaz2
    @arthurbaz22 жыл бұрын

    I've studied this in Calculus about four years ago, but never actually learned it. This helped a lot, thank you!

  • @vahegizhlaryan5052
    @vahegizhlaryan50523 жыл бұрын

    Certainly the best explanation of DD I've seen so far) I had several "wow" moments during this video)

  • @yashmohangupta5379
    @yashmohangupta53793 жыл бұрын

    Holy smokes!!! . how can a student not fall in love with you sir ? . Just struck in awe.

  • @tuncerakilli
    @tuncerakilli15 сағат бұрын

    Gradient vector is such an awesome property when dotted with u unit vector evaluated at a point on a x-y plane in 3D space! Thanks a lot and much appreciated!

  • @Alexanderkermani
    @Alexanderkermani3 жыл бұрын

    This was a stellar video on a topic that I could not wrap my head around. Thank you.

  • @squidsword0
    @squidsword02 жыл бұрын

    Thank you! Everything feels so complicated looking at the notation from far away, but somehow it becomes so intuitive the way you present it. I feel so empowered right now.

  • @sashamuller9743
    @sashamuller97434 жыл бұрын

    the visuals and your teaching really make it!

  • @altaccproxy9890
    @altaccproxy98903 жыл бұрын

    Incredible explanation! So detailed and easily understandable!

  • @derickblacido2267
    @derickblacido22673 жыл бұрын

    Thanks so much Dr Trefor. I was stumbling on this topic for about a month withouth getting the gist of the formula IN GEOMETRICAL terms. Now I can see ligth in my seemingly enduring night. Greetings from Peru.

  • @fraserpye9667
    @fraserpye96679 ай бұрын

    This man is a genius at geometric intuition for calculus. Help me alot, thank you.

  • @___SSS___
    @___SSS___3 жыл бұрын

    Maths is more fun if we can visualise it rather than mugging up formulae . We need teachers like you . 😍😍😍😍😍👏

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    thank you!

  • @user-wu8yq1rb9t
    @user-wu8yq1rb9t2 жыл бұрын

    When I watched your videos, my feeling is changing, and I know why! It's because of harmony! There is a beautiful harmony on your Math and your teaching. I take an oath, Everytime I'm watching your Math at first I enjoyed and then I'm learned. You can change my mood! (It means a lot for me) Thank You SoOoOo Much Teacher ❤️ ((I'm sorry, I forget to say hello !!! Hello teacher))

  • @iskur_
    @iskur_3 ай бұрын

    I'm and engineering undergrad and I had no idea how to solve these questions without overcomplicating it until I saw your videos. Really appreciate the videos and how you also talk about the theory behind the equations.

  • @jadkhalil9263
    @jadkhalil92632 жыл бұрын

    You make calculus easy to understand and fun, keep up the good work!

  • @mirandagonzalez5586
    @mirandagonzalez55864 жыл бұрын

    Great video. I am watching this during my attempt to stay accountable in my semester during COVID-19 and you are really helping me not only to understand better but also to stay interested in this subject Thanks!

  • @guitarttimman
    @guitarttimman4 жыл бұрын

    This is a great demonstration. Thank you.

  • @blankspace1959
    @blankspace19592 жыл бұрын

    amazing content, I always appreciate a skilled mathematician.

  • @leadtoexemplify
    @leadtoexemplify3 жыл бұрын

    Dr Trefor, many will remember you for life time. God bless you.

  • @levimungai1846
    @levimungai1846 Жыл бұрын

    The normal partial derivative is a special case of directional derivatives where you dot the gradient of F with the common unit vectors(i,j,k) or(1,1,1). Your explanation is very insightful.Great video

  • @LudusYT
    @LudusYT4 жыл бұрын

    Hey man, I love your videos! Quick question, how do you make those graphs & animations? Python I assume?

  • @LudusYT

    @LudusYT

    4 жыл бұрын

    Trefor Bazett - Sweet thanks!

  • @danamvenkata
    @danamvenkata3 жыл бұрын

    i have been searching for simple detailed explanation since very long before i found this.... Thank you very much

  • @a.b.6677
    @a.b.66776 ай бұрын

    Wow, brilliant & beautiful, I watched the video 2 or 3 years ago, & I still enjoy going back to it, kudos Professor

  • @jacobvandijk6525
    @jacobvandijk65254 жыл бұрын

    Nice combination of graphs and equations. Good stuff!

  • @madhavkawagucci8539
    @madhavkawagucci85393 жыл бұрын

    why do good teachers and professors exist only online :(. Amazing video

  • @carultch

    @carultch

    Жыл бұрын

    Trefor teaches in person as well.

  • @praveenbethini7126
    @praveenbethini71263 жыл бұрын

    I wish I had a maths teacher like you THANK YOU VERY MUCH 🙏

  • @siwasoontreerat6125
    @siwasoontreerat61252 жыл бұрын

    Best directional derivative explanation. I once learn this when I was in engineering school but I have no idea what does it mean. Now I clearly understand it. Thank you. ^ ^

  • @DrTrefor

    @DrTrefor

    2 жыл бұрын

    Glad it helped!

  • @tanayasharma7776
    @tanayasharma77763 жыл бұрын

    the visual explanation helped me a lot ,I'm extremely happy for some reason after watching this video, thanks a lot.

  • @arnavbhavsar8567
    @arnavbhavsar85673 жыл бұрын

    Earlier I didn't understand this but now I appreciate how beautiful calculus is

  • @SUMITKUMAR-ox5gg
    @SUMITKUMAR-ox5gg Жыл бұрын

    Very well explained with proper intuition with real graphs There was a lot of help while understanding with graph Things get more real and understandable when done with actual graphs

  • @abdulghanialmasri5550
    @abdulghanialmasri55502 жыл бұрын

    You are really one of the best teachers.

  • @shanmukh3174
    @shanmukh317410 ай бұрын

    I have never seen this kind of detailed and articulate explanation Thanks a lot sir 🙏

  • @bitbyte8177
    @bitbyte81773 жыл бұрын

    4:57 That's what she said.

  • @ycc_j
    @ycc_jАй бұрын

    Such clear explanation. I couldn’t understand anything my professor said in class but you made it so easy to learn. Thank you so much!

  • @anshikatyagi6533
    @anshikatyagi65333 жыл бұрын

    The animation was amazing and the way u explained was really nice, we are today complaining abt this online education whereas mentors like had been acing this skill since forever, just WOW

  • @dianafarhat9479
    @dianafarhat94794 ай бұрын

    All channels explain the concepts, but never solve p-sets and think out loud. Your explanation is amazing, would really love to have such videos.

  • @sarvanray3971
    @sarvanray39713 жыл бұрын

    Have never seen such a logical explanation.

  • @aldoperez8551
    @aldoperez85514 жыл бұрын

    Beautiful Explanation. Thank u so much

  • @leadtoexemplify
    @leadtoexemplify3 жыл бұрын

    I am surprised that only 1.8k thumbs up when 38k people watched it. This video deserves 38k thumbs ups.

  • @irfanelahi1384
    @irfanelahi1384 Жыл бұрын

    Maza Agiya Bahi sahb❤👍

  • @waqasmuneer7951
    @waqasmuneer79512 жыл бұрын

    Amazing Dr Trefor. The combo of 3blue 1 brown + Dr Trefor= Mastery of the subject.... No need to go anywhere.

  • @walac
    @walac3 жыл бұрын

    Best explanation of directional derivatives I’ve ever seen!

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    Thank you!

  • @SathanaST
    @SathanaST3 жыл бұрын

    Wish others that are struggling find this video, Thank you for making the video.

  • @edgbaston149
    @edgbaston1493 жыл бұрын

    I am so happy KZread recommended me your videos.😊 Lots of love from India 🇮🇳❤

  • @asme212
    @asme2122 ай бұрын

    Very illustrative and visual. Thank you.

  • @alicebobson2868
    @alicebobson2868 Жыл бұрын

    i always come to your channel whenever im stuck on a topic, you have the best explanations ever!!! thanks!

  • @ayushthada9544
    @ayushthada95443 жыл бұрын

    I had some confusion over differential surface traversal and I ended up on your video. It is a great help. Thank you for posting these amazing videos.

  • @henriquenunes7196
    @henriquenunes71962 жыл бұрын

    Thank you. Important stuff made simple by your expert video. Outstanding.

  • @temesgentesfaye9584
    @temesgentesfaye95845 ай бұрын

    Clear & concise. 👏

  • @yashodabhattarai4206
    @yashodabhattarai42062 жыл бұрын

    Wow, this is extraordinary explanation 👏👏👏

  • @yuheonjoh1336
    @yuheonjoh13364 жыл бұрын

    Just AMAZING! Thank you!!!

  • @xiu8548
    @xiu85484 жыл бұрын

    Cool animation!!!!!! I understand it right away! !

  • @reubenjames8836
    @reubenjames88364 жыл бұрын

    great stuff dude! deserves more attention

  • @codedoc1046
    @codedoc10464 жыл бұрын

    Thanks this cleared things up for me.

  • @abhayranjith
    @abhayranjith3 жыл бұрын

    I wasn't able to understand anything from class for the topic of partial derivatives, but I'm starting to understand now, thanks to your videos

  • @Inkidinkichi
    @Inkidinkichi3 жыл бұрын

    I really wished if you were my tutor! Until now I was just memorizing those formulas! Thank-you sir! Love from india!

  • @ssoomi
    @ssoomi3 ай бұрын

    dude you just saved my life. thank you so much 🙏🙏

  • @bobbysokhi7296
    @bobbysokhi7296 Жыл бұрын

    Amazing Video ! Supplementing this with my lecture notes ! Thank you professor.

  • @cherylzhang1189
    @cherylzhang1189 Жыл бұрын

    Your diagram was so helpful!! I have been struggling to understand the idea of directional derivatives and this video helped so much!

  • @solmaths
    @solmaths2 жыл бұрын

    Simply fantastic !

  • @blymark83
    @blymark833 жыл бұрын

    This is a wonderful video! The visuals are just about perfect, and your using the chain rule to inspire the dot product formula is quite lovely! As a fellow university educator, I've stumbled upon a number of your videos previously and this is among my favorites! You're providing a significant service to the undergraduate mathematical community! Your efforts are appreciated.

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    Thank you so much for your kind words:)

  • @marlorizkalla5889
    @marlorizkalla5889 Жыл бұрын

    So great way explaining this lesson , Very well done prof .

  • @doeunkwon4607
    @doeunkwon46073 жыл бұрын

    Thank you so much, Dr. Bazett

  • @sudarshanv9797
    @sudarshanv97972 жыл бұрын

    This one video cleared all my questions on multivariate calculus

  • @subhamadhikari
    @subhamadhikari7 ай бұрын

    The explanation was concise and very clear.

  • @joaomattos9271
    @joaomattos9271 Жыл бұрын

    Fantastic way of teaching!!! I recommend the classes here in Brazil!

  • @nuthakantirohan4685
    @nuthakantirohan46852 жыл бұрын

    incredible i was strugling to understand this by reading and visiualizing thank u so much nice explanation along with the killer graphics

  • @curiousman1812
    @curiousman18123 жыл бұрын

    You Nailed It !

  • @julioreyram
    @julioreyram3 жыл бұрын

    Brilliant explanation, thank you very much

  • @Junker_1
    @Junker_13 жыл бұрын

    Thanks for all this wonderful explanation.

  • @alijoueizadeh2896
    @alijoueizadeh28966 ай бұрын

    Thank you for your time and effort.

  • @shuvohasan8223
    @shuvohasan82232 жыл бұрын

    You're the greatest teacher I never had... ❤❤❤

  • @codyr9951
    @codyr99512 жыл бұрын

    Great explanation!

  • @mirmos
    @mirmos Жыл бұрын

    Thank you for this beautiful advanced explanation. Both animations and expressions were excellent :)

  • @curiousman1812
    @curiousman18123 жыл бұрын

    Mind blowing !

  • @youssefdirani
    @youssefdirani2 жыл бұрын

    Thanks a lot Dr.

  • @xxyhop
    @xxyhop3 жыл бұрын

    Very nice explanation, thank you!

  • @jeankayembe5775
    @jeankayembe57754 жыл бұрын

    You’re the best!!!!! Thank you so much for your help 🙂

  • @psiandschrody4160
    @psiandschrody41608 ай бұрын

    Thank you! This video was very helpful!

  • @saralewis99
    @saralewis993 жыл бұрын

    Love your passion!

  • @norapatharjanurak1212
    @norapatharjanurak12122 жыл бұрын

    Thank you 😀. This video helps me alot.

  • @alizerg
    @alizerg Жыл бұрын

    Thanks Doc, this was really helpful.

  • @sumitkumarsahoo7601
    @sumitkumarsahoo76013 жыл бұрын

    thanks, great intuition great teacher, well done sir

  • @mostafakooti7729
    @mostafakooti77292 жыл бұрын

    Very nice Easy to understand

  • @rutika17
    @rutika173 жыл бұрын

    Wow🤩 best explanation