Partial Derivatives and the Gradient of a Function

We've introduced the differential operator before, during a few of our calculus lessons. But now we will be using this operator more and more over the prime symbol we are used to when describing differentiation, as from now on we will frequently be differentiating with respect to a specific variable, and we will have to keep track of which one it is. This leads us to the concept of partial derivatives. Although partial differential equations sound like extremely advanced math, and they will get pretty hairy a little later in the series, they're aren't too daunting when just going over their definitions, so let's see what they are and also learn about the gradient of a function, which involves partial derivatives.

Script by Howard Whittle

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[KidDroskii]

"The gradient is kind of like a slope for a higher-dimensional function" is just what I needed to hear to conceptualize this. Thanks!

[adityaadit]

Best 10 minutes and 56 seconds of my life. Such a clear explanation!

[davidbowman]

So good this explanation makes MIT lectures look like an overpriced DLC pack

[onesun]

Gradient: A vector made up of all the partial derivatives of the function. Thank you!

[strugglingcollegestudent]

This man carried me through general chemistry, calculus II and now calculus III. I can't thank you enough for teaching me math.

[kahdargo]

This is awesome. Feel like I finally understand the gradient now.

[radiacia_]

dude, you are capable of explaining multivariable calculus to a 15 year old so that he can actually solve questions, youre a God (I'm the 15 year old)

[jackanderson]

I love how clear and concise your explanations are!

[danielcheong]

this is what you call a video. One of the best teaching videos I've ever watched

[StephenGillie]

Calculus has been independently created/discovered at least 4 times (Pascal has a programming language named after him for his version) and thus we have 4 completely independent, yet internally consistent, sets of notating these concepts. Why did it get reinvented? Lack of local higher mathematics textbooks and education. Thank you for helping to fill this void in the current age, and making a 5th time unnecessary.

[pulpettedilmare]

You rock man! gracias amigo. Im so happy to finally understand it

[alejandroalmarza]

Profesor You are amazingly clear…like all my colleagues here say your 10:57 seconds video summarized hours of calculus classes.. my admiration to you. Thanks

[josephabboud]

Thank you for all your great videos! I'm studying for finals right now and your videos are infinitely better than my professor who lectures online from his bed. You make it so easy to understand in your great verbal and visual explanations, and your videos bring a lot of fun back into learning! I'm into engineering and I love learning through your videos on biology and astronomy and anything really, because learning is fun and awesome. You're a great teacher, thanks for doing such an amazing job :)

[idealthinker]

He taught in such a visual way... !

I couldn't "understand" this concept in my 6 months course of Partial Differential Equations. So I just crammed some formulas and just passed the exams.

[goutsugoutsu]

Oh thank you so much! After 19 years I can finally picture it!!!

[te-kowski]

Literally the best explanation. Trying to do a project where partial derivatives come up, and I needed a quick refresher.

[devanshujoshi]

This is highly underrated
Ngl I’m lucky i found this 🔥 I subscribed❤️

[Deepak-pixx]

Thank you so much. Finally understood the real meaning of partial derivative and gradient. 😇

[gandalfthegaytwotowerdestr]

What a Life saver, thanks so much, professor

[GAment_]

I just went down and liked every comment that was positive on this video. Its the only way to extend my appreciation! Thanks man!