How To Find The Directional Derivative and The Gradient Vector

This Calculus 3 video tutorial explains how to find the directional derivative and the gradient vector. The directional derivative is the product of the gradient vector and the unit vector. To find the gradient vector, you need to find the partial derivatives of f with respect to x, y, and maybe z for a 3 variable function.
Lines & Planes - Intersection: • How To Find The Point ...
Angle Between Two Planes:
• How To Find The Angle ...
Distance Between Point and Plane:
• How To Find The Distan...
Chain Rule - Partial Derivatives:
• Chain Rule With Partia...
Implicit Partial Differentiation:
• Implicit Differentiati...
________________________________
Directional Derivatives:
• How To Find The Direct...
Limits of Multivariable Functions:
• Limits of Multivariabl...
Double Integrals:
• Double Integrals
Local Extrema & Critical Points:
• Local Extrema, Critica...
Absolute Extrema - Max & Min:
• Absolute Maximum and M...
________________________________
Lagrange Multipliers:
• Lagrange Multipliers
Triple Integrals:
• Triple Integrals - Cal...
2nd Order - Differential Equations:
• Second Order Linear Di...
Undetermined Coefficients:
• Method of Undetermined...
Variation of Parameters:
• Variation of Parameter...
________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/

[@wetrathours9140]

thank you. my calc test opens in 7 minutes and this was my introduction to the material. i'll credit you when i graduate

[@matyastoulemonde3622]

Damn bro I hope you passed!

[@wetrathours9140]

@@matyastoulemonde3622 i did! thank you!

[@BossKing1243]

@@wetrathours9140 W

[@theofficialchan]

Enough to give a young bachelor hope

[@michaelarc2792]

My mid exam starts in hour and half and I haven't studied yet , f*ck procrastinating

[@user-hv8kv8qx7v]

True, I do not speak English, but your explanation is clear ar, even if someone who watches the passage does not speak English understand, thank you, and may God reward you a thousand good

[@sateleim]

THIS IS LITERALLY INSANE LIKE ITS SO MUCH EASIER THAN I THOUGHT

[@daniel4960]

10 hours till mathematics exam. Organic chemistry tutor it is :D

[@manabsaha2733]

It's only 1 hour for me :P
(Small Class test though)

[@keziaowusuankomah5065]

This teacher is helping we the students who by means of double track system are not spending much time in school.. Thanks a lot👍

[@lordanonimmo7699]

@Alan Naranjo He is even helping students that are good at math,this helps them understand better and faster.

[@chickenconnoisseur2725]

Im not taking calc yet, but I just wanna say thanks for helping me in dozens of other videos, really appreciate your commitment in helping others

[@itsjustferaas2680]

My professor couldn't make it that simple! You sir are a lifesaver ❤

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for a solid explanation on How to Find the Directional Derivative and the Gradient Vector in Multivariable Calculus/Calculus Three. This topic is simple to follow and understand from start to finish. This is an error free video/lecture on TH-cam TV with the Organic Chemistry Tutor.

[@SUNSHINE25150]

❤❤❤❤🎉🎉🎉🎉🎉We gotta give you all the love and flowers coz wow man you deserve them...best tutor there ever is...your videos are short and straight to the point 😊👌🏽they make PERFECT SENSE...THANK YOU SO MUCH ❤❤❤

[@dustinlouisos5745]

I JUST had a class on this yesterday. Perfect timing for me!

[@inshal6420]

TheOrganicChemistryTutor for when im cramming and Professor Leonard for when I have time to learn

[@HeyKevinYT]

For those wondering why multiply with a, b, and c: the general formula for the directional derivative of f(x,y,z) in unit vector *v* is
∇f · *v*
which is why each component of f is multiplied with the corresponding component of *v*.

[@user-rx6zl9mr3k]

where are you getting those cos and sine

[@emanuelocasio4641]

Thank you for sharing these videos I use them just before my Calculus 3 class to help me understand the topic.

[@CM-dx6xu]

Cosine of Pi/3 = Cosine of 60°, which is 1/2. He should be correct, and you are wrong.

[@emanuelocasio4641]

@@CM-dx6xu Ok thanks I see.

[@lidyasolomon5557]

Thank you so much!!! YOU"RE SAVING MY CALC 3 GRADE!

[@Hackslooi0128]

could you do a directional derivative of:
1. Gradient vector: Maximizing rate of change
2. Gradient vector: Normal to level curve/surface

[@antx1026]

No... Don’t you have some “getting laid” to do?

[@Cqyll]

@@antx1026 Sounds like its you that needs to get laid.

[@zakthayer9315]

yeah the gradient is used in normal and constrained optimization problems, o chem tutor has videos on it! (basically to get the 'critical points' u set each part of the gradient equal to 0 then evaluate, then u plug in the point to the original function, calculate this weird thing called D, and depending on if it's positive or negative know if u have a local max or min, the greatest and least are ur absolutes

[@LearnEngineering678]

th-cam.com/video/l6YOfcOf_3c/w-d-xo.html

[@inthebackwiththerabbish]

i put my life in your hands, organic chemistry tutor

[@coldlama8370]

This man's retirement better be funded by all of us who get sick ass careers from his teachings.

[@joshbullis2322]

Thank you so much! I’ve been struggling in Calculus 3. Do you have any other videos on Cal 3?

[@justso1337]

The Organic Chemistry Tutor for life

[@russthebus1990]

So helpful, literally saved my life!

[@kanivakil198]

How do you find that the direction derivative is cos and sin of pi/3? If I see a problem like this I just assume where x is the given theta?

[@koyeb832]

I wanted to ask the same question also. Hopefully someone answers

[@unnameduser624]

its because (cos, sin) are the coordinates to the unit circle. i think it's different if the problem gives you a point rather than an angle. not sure though.

[@lanomusambazi-tx2eg]

I have really learnt today.

[@godabhi8599]

I literally love you ,you are my savior angel

[@muhammadhaitham6892]

thank you bro , you are a gift from god to us

[@MMYLDZ]

You sure know a whole lotta math for and organic chemistry tutor.

[@muteahmdv]

It helped me a lot thank you very much. I have a midterm for wednesday, and this video just saved me..!!!!

[@caesarcastelo9458]

Thank You very much for sharing your talents sir and may God bless you in all your hardworks . Blessings...

[@user-cx1fy5yd3j]

Thank you sir.

[@Gasgar800]

Thaaaaanks ! midterm in 2 days, this helps a lot :)

[@Hackslooi0128]

Thank you, am looking for this, can’t understand in class.

[@gu4650]

organic chemistry tutor i love you

[@masonp1599]

I know I say this all the time but....u da man

[@lizzyliza4705]

Thank you. Your videos always come to my rescue

[@Decor4720]

😂😂😂😂

[@phil97n]

Thank you for sharing your knowledge, this is great stuff for a beginner like myself

[@salinalamasl]

I have come to say you have literally made something that makes no sense into a lot of sense. Thank you so much and I hope you are taken good care of by a lot of good karma.

[@cht5086]

I have been watching your videos since I was in college, now I am a University student. Many teachers just express and demonstrate their knowledge instead of explaining things in an easy way!. Like they want to prove Monalisa’s nose without showing her face and make things complicated! While a good teacher can explain 20 pages in 3 minutes.

[@malharwable655]

You made it so easy to understand!!! Thankyou!

[@TheFarmanimalfriend]

I was under the impression the each part of the direction vector needs to be divided by the vector's magnitude. In the case of the unit circle, using pi, the magnitude is always 1

[@stogam3550]

Thanks man you number one ❤❤❤

[@user-mx1hm7ju8q]

just paused my teacher and searched for your explanation

[@bowenchamp7162]

Same deal here.

[@lanomusambazi-tx2eg]

Thank you sir for the lecture.

[@salman-oi9bp]

Please can u explain path independence and greens theorem plzzzzz and also line integrals

[@salman-oi9bp]

Also fouriers series plzzz my exams are coming soon will be much much apriciated

[@Riad-Eleid]

Thank you

[@youssefhassan7867]

Thank you 🙏

[@LearnEngineering678]

th-cam.com/video/l6YOfcOf_3c/w-d-xo.html

[@krishgoogol8653]

Thanku ❤️

[@aswinpm8554]

HELPFULL

[@alihakimoglu3242]

Thanks professor, you helped me a lot

[@zhandoshumyrbek9814]

Exactly two years later I am watching this video😊

[@iced751]

When I eventually graduate I'm donating to you

[@jdoe8162]

You're my hero

[@amhakabaw]

Thank you sir you are smart bro 🙏🥰🥰

[@godspeedninja4231]

I thank you for helping me in my college career. its my 3rd year im almost there.

[@BossKing1243]

Bless of my g

[@BossKing1243]

Best of luck g

[@rendelsolares5892]

Thank you so much

[@SamB782]

OCT is the king of night-before cram sessions

[@thetwogoats6851]

Great!, thanks for always helping

[@TheAwamia]

you're a life saver

[@TerseFilms]

We need to get this guy on Ellen!

[@yanjumitra9825]

Someone please clear this to me - why would we have to calculate the angle on Sin & Cos but not on tan /cot/sec ???

[@briannguyen5057]

very helpful, thanks

[@grantglessing3668]

He literally don’t miss

[@Lexyvil]

Can anyone help me know how to obtain a fraction result when computing cos or sin on a calculator? As shown at the beggining of the video for solving the unit vector.

[@michaellaankrah2843]

Hey there, make sure your calculator setting is in rad not deg. Then when you input the cos and sin you’ll get your answer.

[@leonardshipandeni6038]

when finding the unit vector should we always start with sin first or I can start with any of my choice?

[@lalanpandey5608]

Thanks

[@shukkkursabzaliev1730]

Simply the best!

[@Umareineacademia0196]

thanks mr superman

[@user-dd9zo4mz8r]

Bro can teach quantum physics to kids 🗿

[@dzmitryk9658]

Awesome! Thank you!

[@LearnEngineering678]

th-cam.com/video/l6YOfcOf_3c/w-d-xo.html

[@BalaNate]

If the unit vector, u is given, is it necessary to normalize it first before doing further calculations?

[@beckettgalloway7155]

Why normalize the vector it’s in the direction of? Would changing the magnitude not change the roc?

[@aao_seekhen1]

Love you sir

[@user-df7fn3ro4p]

You are always giving angle theta can you plz say with what the function make that angle.ex: like x axis or y axis like that plz reply if anyone also knows

[@jesussaquin6266]

May someone explain the difference between Directional Derivatives and Gradient Vector

[@wobbler2536]

How is it different if the question asks “in the direction (theta=something) to the (x,y or z) axis?

[@rafiyamajeed1102]

Thank you sir

[@LearnEngineering678]

th-cam.com/video/l6YOfcOf_3c/w-d-xo.html

[@iannikolas5171]

In this case, (1,2) is the initial point, right?

[@adtyamshra]

thankyou sir

[@henryy6918]

Wonderful!

[@mfarooqsheikh4523]

love u hogya wada wada

[@albatros1802]

My Goat

[@blaisetedonleukeu6744]

Please what would have happened if you were given in 3D the vector in the first question what would have been "c"

[@Aqwtiny]

i got 100/7 for number 2 part b.. X component is 3y^3+2z^2 using product rule. can anyone double check this for me

[@eriedului]

it's actually 3y^3-2z^2. There is no product rule when computing that partial derivative.

[@user-zl2ml2ow6b]

perfect

[@zombieKILz_115]

5:18 Magitude i choose you

[@shireenkhan6847]

everyone in comments are studying this in Cal 3 meanwhile i am studying it in cal 2

[@MAUAWENGE-sw2bw]

Me 2😢

[@ChandlerChandler]

why couldn't my prof teach like this?

[@kegtuwa]

go to guy for quarantine

[@wayneashleyklaase9375]

Lovely 🌹

[@giftsadique1806]

Where's the denominator of 7 coming from?

[@Diego0wnz]

why is this in my calculus 1 class???

[@stasanstasaynovich23]

Wait, in #3, weren't we supposed to find the magnitude of the vector to make it a unit vector, as we were calculating directional derivative?

[@marcusmoulia639]

yes

[@Lexyvil]

What is the difference between the (...) and notation when it comes to vectors? Or is it only a question of preference? Thank you.

[@axeltorbenson8533]

Late reply but (...) is used for points and is used for vectors.

[@Jasmine-lg6xb]

Tnx

[@jace4958]

Thnx:))

[@omarwhatever6542]

if i won the lottery at some point a few racks are getting directionally derivated to ur house

[@nullynn1887]

3:39 to 4:36 (1st question)

[@jackiel.5805]

20:52 i think df/dz is 6xz^2-9yz^2 is it not?

[@christosadamopoulos1015]

you did 3^2 instead of 3*2

[@wiilhoog8804]

welldone