Partial derivatives of vector-valued functions | Multivariable Calculus | Khan Academy

Partial Derivatives of Vector-Valued Functions

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Multivariable Calculus on Khan Academy: Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions.

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[sheilferzepeda]

Thank you very much, Sal and Khan Academy. There aren't as many views or comments here so I'm going to take the liberty to drop more resources for other students reviewing this material come study time.

if you're looking for more resources on partial derivative applications check out:

Pauls notes online (if you like learning by easy reading)

Try using symbolab if you like learning problems step by step (it's a step by step calculator).

or of course Khanacademy's module for learning too is very comprehensive. If you like using his youtube videos, you'll love his organization's teaching modules. It's even more involved than just being lectured through these awesome vids.

[mycityofsky]

Thank you, this is so clear and concise. I struggled for a while when I was reading on Wikipedia about partial derivatives of vector-valued functions, there were so much mathematical jargon in the definition in order to tell readers what it was. I kept searching and searching until I realized there might be something about it on YouTube. Then I searched it on YouTube and I found your lecture. So simple and intuitive. Amazing job you did right here!

[brendanhall]

What's the difference between the differential of s and the partial differential of s. Is that why the partial of s and the differential of s don't cancel out?

[OverlyCuriousEngineer]

Thanks for the great vid, Sal. I want a suggestion, what book should i use to study Multivariable calculus? A book thats simple and easy to get. We are using Advanced Engg Math by Kreyszig and its literally the worst math book when it comes to explaining. Thanks.

[safdarabbaskhan]

Great video. I saw this clip after having watched the clip of surface integrals. The clip of surface integrals was very helpful to me to understand the concept of surface integral. This clip P.D.V.V.F., I saw it due to its reference in surface integrals. Booth of them are very great. Thanks a lot man.

[reik]

great timing sal, thanks ;) I'm doing this stuff right now in Analysis II. (or multivariable calculus as you call it)

[justanon]

why is it an issue to replace delta s by ds? I cant understand

[jasonmiller]

I know that variables could represent anything, so this doesn't affect calculations, but since t often denotes time, and s often denotes distance, how would you interpret a function of s and t on a 3d graph geometrically? Why is s not just x, y, or z? Thanks in advance.

[AnkitkumarKumar-vbbm]

sar please write in big letter, and give some gap b/w the numbers.

[bslaozora]

cant even understand why is that crazy lol
I always treat dy or dx as mere numbers, just a very small one....
P.S.physics guy