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.

Angle Between Two Planes:

Distance Between Point and Plane:

Chain Rule - Partial Derivatives:

Implicit Partial Differentiation:

________________________________
Directional Derivatives:

Limits of Multivariable Functions:

Double Integrals:

Local Extrema & Critical Points:

Absolute Extrema - Max & Min:

________________________________
Lagrange Multipliers:

Triple Integrals:

2nd Order - Differential Equations:

Undetermined Coefficients:

Variation of Parameters:

________________________________
Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

[wetrathours]

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

[رقية-فه]

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

[a_zhongbaode]

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

[andrewrivera]

Thank you so much, Im taking this class as a Junior in hs and my professor is not explaining gradients well. Thx for the help

[keziaowusuankomah]

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

[itsjustferaas]

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

[daniel]

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

[chickenconnoisseur]

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 <3

[dustinlouisos]

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

[inshal]

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

[georgesadler]

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 YouTube TV with the Organic Chemistry Tutor.

[emanuelocasio]

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

[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*.

[SUNSHINE]

❤❤❤❤🎉🎉🎉🎉🎉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 ❤❤❤

[Hackslooi]

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

[lidyasolomon]

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

[joshbullis]

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

[inthebackwiththerabbish]

i put my life in your hands, 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..!!!!