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

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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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Опубликовано:

16 ноя 2019

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Комментарии : 357

@subse5371 3 года назад

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

@kafuu1 10 месяцев назад

thats the power of Internet

@mikzin630 9 месяцев назад

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

@shivangsingh5834 6 месяцев назад

@@mikzin630😂😂

@prathikkannan3324 Месяц назад

@@mikzin630 It's easy. You can literally memorize your way through single variable calculus if you are solid in algebra.

@broqentoys 4 года назад

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

@gonderage 4 года назад

Yo, me too!

@HorizonSpeed26 3 года назад

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

@shadabansari9121 3 года назад

@@gonderage Ya , i long too

@shadabansari9121 3 года назад

@SHADAB ANSARI , u 2 :)

@mosalethoba5267 3 года назад

He's your teacher thanks to the internet

@jaydean5243 3 года назад

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 года назад

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!

@Hinchey613 2 месяца назад

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

@DrTrefor 2 месяца назад

Glad it helped!

@chetanraina5649 4 года назад

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

@dushyantsengar9381 4 года назад

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 года назад

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

@effizienzlizenz 4 года назад

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

@pultural 3 года назад

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!

@siwasoontreerat6125 2 года назад

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 года назад

Glad it helped!

@muhammadharoonlatif5154 3 года назад

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

@farhansadik5423 3 дня назад

A genius of teaching. You're a special gift to us students, thank you dr. Bazett :)

@AndyOrtiz93 Месяц назад

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

@user-jc2uv4re8h Месяц назад

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.

@user-wu8yq1rb9t 2 года назад

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))

@darkphoenix_007 Год назад

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

@pipertripp 4 дня назад

pure gold. Great presentation. I'm really enjoying working through all the partial derivative vids in the play list. Reviewing them before moving on to the optimisation videos.

@squidsword0 2 года назад

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.

@vahegizhlaryan5052 3 года назад

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

@tuncerakilli Месяц назад

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!

@ycc_j 3 месяца назад

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!

@blymark83 3 года назад

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 года назад

Thank you so much for your kind words:)

@MinhLe-se6bs 5 месяцев назад

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

@a.b.6677 8 месяцев назад

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

@walac 3 года назад

Best explanation of directional derivatives I’ve ever seen!

@DrTrefor 3 года назад

Thank you!

@derickblacido2267 3 года назад

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.

@yashmohangupta5379 3 года назад

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

@donlansdonlans3363 4 года назад

Omg finally I understand this

@calebmossgrove8022 Год назад

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 Год назад

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

@felipao2134 Год назад

@@gabrielcruzati3717 Em Portugal tb

@sujal1548 Год назад

@@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. Год назад

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

@iskur_ 4 месяца назад

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.

@madhavkawagucci8539 3 года назад

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

@carultch Год назад

Trefor teaches in person as well.

@fraserpye9667 10 месяцев назад

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

@Alexanderkermani 4 года назад

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

@leadtoexemplify 3 года назад

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

@arthurbaz2 2 года назад

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

@SUMITKUMAR-ox5gg Год назад

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

@ayushthada9544 3 года назад

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.

@rockyjoe3817 Год назад

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

@dianafarhat9479 6 месяцев назад

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.

@mirandagonzalez5586 4 года назад

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!

@waqasmuneer7951 2 года назад

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

@edgbaston149 3 года назад

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

@praveenbethini7126 4 года назад

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

@nazatkabir3442 3 года назад

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

@DrTrefor 3 года назад

Glad you enjoyed!

@levimungai1846 Год назад

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

@SathanaST 4 года назад

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

@sashamuller9743 4 года назад

the visuals and your teaching really make it!

@Inkidinkichi 3 года назад

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

@asme212 4 месяца назад

Very illustrative and visual. Thank you.

@shanmukh3174 Год назад

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

@subhamadhikari 8 месяцев назад

The explanation was concise and very clear.

@abdulghanialmasri5550 2 года назад

You are really one of the best teachers.

@sudarshanv9797 2 года назад

This one video cleared all my questions on multivariate calculus

@tanayasharma7776 3 года назад

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

@leadtoexemplify 3 года назад

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

@sarvanray3971 3 года назад

Have never seen such a logical explanation.

@LudusYT 4 года назад

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

@LudusYT 4 года назад

Trefor Bazett - Sweet thanks!

@jadkhalil9263 2 года назад

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

@danamvenkata 4 года назад

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

@abhayranjith 3 года назад

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

@nuthakantirohan4685 2 года назад

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

@xiu8548 4 года назад

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

@mostafakooti7729 2 года назад

Very nice Easy to understand

@henriquenunes7196 2 года назад

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

@irfanelahi1384 Год назад

Maza Agiya Bahi sahb❤👍

@jacobvandijk6525 4 года назад

Nice combination of graphs and equations. Good stuff!

@shuvohasan8223 2 года назад

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

@yashodabhattarai4206 3 года назад

Wow, this is extraordinary explanation 👏👏👏

@alicebobson2868 Год назад

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

@altaccproxy9890 3 года назад

Incredible explanation! So detailed and easily understandable!

@ssoomi 5 месяцев назад

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

@marlorizkalla5889 Год назад

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

@anshikatyagi6533 3 года назад

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

@guitarttimman 4 года назад

This is a great demonstration. Thank you.

@___SSS___ 3 года назад

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

@DrTrefor 3 года назад

thank you!

@sumitkumarsahoo7601 3 года назад

thanks, great intuition great teacher, well done sir

@blankspace1959 2 года назад

amazing content, I always appreciate a skilled mathematician.

@joaomattos9271 Год назад

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

@hugochavez8797 3 года назад

great video, great explanation, thanks form Mexico.

@DrTrefor 3 года назад

Thank you!!

@rutika17 3 года назад

Wow🤩 best explanation

@cherylzhang1189 Год назад

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

@temesgentesfaye9584 7 месяцев назад

Clear & concise. 👏

@codyr9951 2 года назад

Great explanation!

@weekendfriday22 2 месяца назад

this helps a lot i am taking calc 3 in the summer in 6 weeks, and basically, i have to study 2 chapters a 2week , these videos help a lot on the question ," why we do this"

@weekendfriday22 2 месяца назад

week not 2week

@norapatharjanurak1212 2 года назад

Thank you 😀. This video helps me alot.

@ilong4rennes Год назад

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

@ghostfrom1950 2 года назад

such a difficult thing to conceptualize is deserving of such graphics as these. Why do remote learning professors suck so much?? This helped a ton. I was still shaking on my geometric understanding of the partial deriv.