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

Рет қаралды 166,933

4 жыл бұрын

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: 348

@subse5371 3 жыл бұрын

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

@kafuu1 8 ай бұрын

thats the power of Internet

@mikzin630 7 ай бұрын

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

@shivangsingh5834 4 ай бұрын

@@mikzin630😂😂

@broqentoys 4 жыл бұрын

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

@gonderage 4 жыл бұрын

Yo, me too!

@HorizonSpeed26 3 жыл бұрын

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

@shadabansari9121 3 жыл бұрын

@@gonderage Ya , i long too

@shadabansari9121 3 жыл бұрын

@SHADAB ANSARI , u 2 :)

@mosalethoba5267 3 жыл бұрын

He's your teacher thanks to the internet

@jaydean5243 3 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

@v-doc5230 3 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!

@dushyantsengar9381 4 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 :)

@samyakgupta4301 3 жыл бұрын

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

@effizienzlizenz 4 жыл бұрын

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

@chetanraina5649 4 жыл бұрын

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

@muhammadharoonlatif5154 3 жыл бұрын

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

@ycc_j 27 күн 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!

@pultural 3 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!

@MinhLe-se6bs 2 ай бұрын

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

@arthurbaz2 2 жыл бұрын

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

@Alexanderkermani 3 жыл бұрын

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

@rockyjoe3817 Жыл бұрын

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

@squidsword0 2 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.

@darkphoenix_007 Жыл бұрын

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

@iskur_ 2 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.

@derickblacido2267 3 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.

@vahegizhlaryan5052 3 жыл бұрын

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

@donlansdonlans3363 4 жыл бұрын

Omg finally I understand this

@yashmohangupta5379 3 жыл бұрын

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

@fraserpye9667 8 ай бұрын

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

@sashamuller9743 3 жыл бұрын

the visuals and your teaching really make it!

@praveenbethini7126 3 жыл бұрын

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

@a.b.6677 5 ай бұрын

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

@tanayasharma7776 3 жыл бұрын

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

@user-wu8yq1rb9t 2 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))

@altaccproxy9890 3 жыл бұрын

Incredible explanation! So detailed and easily understandable!

@siwasoontreerat6125 2 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 2 жыл бұрын

Glad it helped!

@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

@danamvenkata 3 жыл бұрын

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

@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

@blankspace1959 2 жыл бұрын

amazing content, I always appreciate a skilled mathematician.

@mirandagonzalez5586 4 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!

@jadkhalil9263 2 жыл бұрын

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

@shanmukh3174 10 ай бұрын

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

@arnavbhavsar8567 3 жыл бұрын

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

@alicebobson2868 Жыл бұрын

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

@ayushthada9544 3 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.

@jacobvandijk6525 4 жыл бұрын

Nice combination of graphs and equations. Good stuff!

@SathanaST 3 жыл бұрын

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

@anshikatyagi6533 3 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

@calebmossgrove8022 Жыл бұрын

As an engineering student who did well in Calc 2. I'm struggling to visualize calc 3 and study for my midterm. This really saved me and it was an amazing explanation. Thanks

@gabrielcruzati3717 Жыл бұрын

Man, you are fine. Here in Brazil, this is my calc II :´)

@felipao2134 Жыл бұрын

@@gabrielcruzati3717 Em Portugal tb

@sujal1548 Жыл бұрын

@@gabrielcruzati3717 I'm guessing it depends on your university because here in Canada, my uni is doing this in calc 2 as well but other universities don't

@Rwko. Жыл бұрын

Yeah ,here in Greece in the particular department im in, multivariable calculus is basically calc ll.

@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!

@abhayranjith 3 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

@madhavkawagucci8539 3 жыл бұрын

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

@carultch Жыл бұрын

Trefor teaches in person as well.

@guitarttimman 4 жыл бұрын

This is a great demonstration. Thank you.

@Inkidinkichi 3 жыл бұрын

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

@henriquenunes7196 2 жыл бұрын

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

@leadtoexemplify 3 жыл бұрын

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

@dianafarhat9479 3 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.

@sudarshanv9797 2 жыл бұрын

This one video cleared all my questions on multivariate calculus

@asme212 2 ай бұрын

Very illustrative and visual. Thank you.

@abdulghanialmasri5550 2 жыл бұрын

You are really one of the best teachers.

@bobbysokhi7296 Жыл бұрын

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

@blymark83 3 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 3 жыл бұрын

Thank you so much for your kind words:)

@marlorizkalla5889 Жыл бұрын

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

@mirmos Жыл бұрын

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

@nuthakantirohan4685 2 жыл бұрын

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

@walac 3 жыл бұрын

Best explanation of directional derivatives I’ve ever seen!

@DrTrefor 3 жыл бұрын

Thank you!

@aldoperez8551 4 жыл бұрын

Beautiful Explanation. Thank u so much

@waqasmuneer7951 2 жыл бұрын

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

@jiminmoon6457 3 жыл бұрын

thank you so much! I've been trying so hard to understand the slope of directional derivatives on the graph! This helped a lot!

@DrTrefor 3 жыл бұрын

Glad it helped!

@LudusYT 4 жыл бұрын

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

@LudusYT 4 жыл бұрын

Trefor Bazett - Sweet thanks!

@joaomattos9271 Жыл бұрын

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

@subhamadhikari 6 ай бұрын

The explanation was concise and very clear.

@ssoomi 3 ай бұрын

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

@codedoc1046 4 жыл бұрын

Thanks this cleared things up for me.

@sarvanray3971 3 жыл бұрын

Have never seen such a logical explanation.

@leadtoexemplify 3 жыл бұрын

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

@edgbaston149 3 жыл бұрын

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

@Junker_1 3 жыл бұрын

Thanks for all this wonderful explanation.

@shuvohasan8223 2 жыл бұрын

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

@alijoueizadeh2896 6 ай бұрын

Thank you for your time and effort.

@julioreyram 3 жыл бұрын

Brilliant explanation, thank you very much

@ilong4rennes Жыл бұрын

thank you so much for the content. this helps me a lot for my calc 3 class.

@___SSS___ 3 жыл бұрын

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

@DrTrefor 3 жыл бұрын

thank you!

@yashodabhattarai4206 2 жыл бұрын

Wow, this is extraordinary explanation 👏👏👏

@psiandschrody4160 7 ай бұрын

Thank you! This video was very helpful!

@jeankayembe5775 3 жыл бұрын

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

@alizerg Жыл бұрын

Thanks Doc, this was really helpful.

@sumitkumarsahoo7601 3 жыл бұрын

thanks, great intuition great teacher, well done sir

@mooseminddayan4650 3 жыл бұрын

Thank you so much. Your pedagogical skills are top-drawer.

@DrTrefor 3 жыл бұрын

Glad you like them!

@yuheonjoh1336 4 жыл бұрын

Just AMAZING! Thank you!!!

@temesgentesfaye9584 4 ай бұрын

Clear & concise. 👏

@doeunkwon4607 3 жыл бұрын

Thank you so much, Dr. Bazett

@nazatkabir3442 3 жыл бұрын

idk why but his way of explaining things is so engaging. it really is amazing 🤩🤩.

@DrTrefor 3 жыл бұрын

Glad you enjoyed!

@xxyhop 3 жыл бұрын

Very nice explanation, thank you!

@xiu8548 4 жыл бұрын

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

@norapatharjanurak1212 2 жыл бұрын

Thank you 😀. This video helps me alot.

@finitecoloring 4 жыл бұрын

What did you use for the graphic moving

@noder8867 4 жыл бұрын

Thank you, clear explanation. I guess if u was not a unit vector, it would still work as s -> 0?

@NicolaasVerhoef Ай бұрын

Fantastic video sir! If you don't mind me asking, which software do you use for the graphing of the functions? Thank you for the great video.

@leeeeee877 3 жыл бұрын

your videos are amazing.thanks a lots for your help.

@vijaysinghchauhan7079 3 жыл бұрын

Your visuals give life to Mathematical concepts. Question: at around 8:57 is gradient born 🐣 from the Directional derivative?

@reubenjames8836 4 жыл бұрын

great stuff dude! deserves more attention

@bitbyte8177 3 жыл бұрын

4:57 That's what she said.

@solmaths 2 жыл бұрын

Simply fantastic !

@saralewis99 3 жыл бұрын

Love your passion!