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/

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

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(Small Class test though)

[@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]

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[@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

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[@RODGERSCHANSA-p7y]

where are you getting those cos and sine

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[@inshal6420]

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

[@Hackslooi0128]

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

[@Gasgar800]

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

[@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.

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

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Thanks professor, you helped me a lot

[@dustinlouisos5745]

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

[@yanjumitra9825]

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

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Thank you 🙏

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[@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

[@cajwan]

you're a life saver

[@thetwogoats6851]

Great!, thanks for always helping

[@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*.

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OCT is the king of night-before cram sessions

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

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

[@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 UA-cam TV with the Organic Chemistry Tutor.

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[@user-mx1hm7ju8q]

just paused my teacher and searched for your explanation

[@bowenchamp7162]

Same deal here.

[@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.

[@a2_zhongbaode718]

For those wondering why unit vector is cos and sin, you can plot a triangle, since unit vector has a magnitude of 1, using cos = adjcent/hypotenuse (aka 1) bring the hypotenuse over you get 1 cos (angle) = adjacent length, similarly for sin you get the opposite value and these maps to your (x,y) values

[@PRITOMACHARJEE-q8l]

Thank you sir.

[@beckettgalloway7155]

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

[@Riad-Eleid]

Thank you

[@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.

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i put my life in your hands, organic chemistry tutor

[@BalaNate]

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

[@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.

[@zhandoshumyrbek9814]

Exactly two years later I am watching this video😊

[@justso1337]

The Organic Chemistry Tutor for life

[@jesussaquin6266]

May someone explain the difference between Directional Derivatives and Gradient Vector

[@aswinpm8554]

HELPFULL

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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.

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Thank you

[@giftsadique1806]

Where's the denominator of 7 coming from?

[@MMYLDZ]

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

[@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?

[@Diego0wnz]

why is this in my calculus 1 class???

[@russthebus1990]

So helpful, literally saved my life!

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I have really learnt today.

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Thanku ❤️

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

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Thank you so much dude you made this look so so easy!

[@shireenkhan6847]

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

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Me 2😢

[@theenairobikid]

We are not able to see the demonstration part is hiding some content.

[@ChandlerChandler]

why couldn't my prof teach like this?

[@Lauranim]

Bruh I'm attending university in South Korea and this is considered Calculus 2 not 3... I'm only on my first year...

[@muteahmdv]

Same as me :(((

[@StarSpliter]

Depends on the school. I know American Unis that definitely consider this calc 2 and some people take it first year as well

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same

[@ManicharanKaigala]

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

[@blaisetedonleukeu6744]

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

[@kerembalc5430]

please give background information about issues. You just give formulas

[@emmanuelokumu7735]

where is 2/7, 3/7, 6/7 coming from

[@iannikolas5171]

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

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Thanks

[@leonardshipandeni6038]

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

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

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yes

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perfect

[@wobbler2536]

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

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