What are derivatives in 3D? Intro to Partial Derivatives

Imagine walking in only the x or only the y direction on a multivariable function f(x,y). The slope in these directions gives the idea of a partial derivative. It's much like the slope of a single variable function is the derivative, it is just now we have more than one direction we can go to. When heading, say, parallel to the x axis this is equivalent to saying the y is constant. This makes computing partial derivatives easy: just take a normal derivative as if the other variable is contant.

Sorry for the bad audio quality on this one!

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This video was created by Dr. Trefor Bazett

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[arnavbhavsar]

Thank you so much for this playlist. It helped me get intuition on my multivariable calculus course

[chyldstudios]

The audio was a bit weird at times. Also nice work on the graphics.

[leronm]

Amazing video! We went through this so fast in my Calc III class that I missed the explanation for "what" a partial derivative was completely. This flushes out a lot of everything we learned that built upon partial derivatives!

[shubhamsatyaprakash]

THANKS FOR NOT BEING IN THE VIDEO, YOU ARE QUITE HANDSOME TO KEEP US DISTRACTED WHILE WATCHING YOUR EDUCATIONAL VIDEOS. JUST KIDDING. KEEP ON DOING YOUR NOBLE WORK

[rockyjoe]

Amazing work!!! Hope to see you coming with more videos :D

[aaravs]

I love watching this out of pure interest while still taking my high school AP calculus BC course!

[yogeshpx]

U r voice, animation everything is amazing

[ismailsevimli]

Really thanks, it was hard to get the big picture of these subjects by studying from a book.

[nicolasdegaudenzi]

YOU ARE A GENIUS, I'M UNDERSTANDING EVERYTHING!!
THANKS FOR EXPLAINING

[GameChanger-bc]

You are repeatedly saying 2-D graph as one dimensional graph and 3-D graph as 2 dimeansional graph ....is it intentionally or a mistake and if it is intentionally could you mention it

[grafzeppelin]

This video is helpful, but I think you should have provided the actual function for f in this case, and provided the specific number for y_0, say, 5, demonstrated that f(x, 5) is in fact the parabola shown, and then extended it to ask, "Ok, but what if we want to know the slope in the 'east' (x) direction, df/dx, NOT specifically at y = 5, leaving y as "y"?" (Then the same for x_0.)

I find that students have trouble perceiving of the notation "y_0" as "a hypothetical constant, instead of a variable" no matter how many times I tell them.

[namex]

Thanks a lot for this series, really helpful and interesting.
The audio is cringy sometimes and its difficult to understand some of the words though.

[vaisuliafu]

really fantastic quality videos - great job

[rohullahakhlaghy]

So what I understood is that we should take derivative of the multivariable function separately for every variable. Is that right?

[stephenbarnard]

Not me binging this playlist 2 days before my calc 3 exam

[ogunsadebenjaminadeiyin]

I ploted the equations on a 3D plot and the differention made meaning graphically as a tangent to the function.

[items]

Professor where are you in the video you're presence make your videos from next level(literally i have no words) but i missed you in this video. Love 💝 from india thank you professor.🙏🙏🙏🙏😇😇😇😇❤️❤️❤️❤️❤️

[SnortsOfHappiness]

Good video and appreciate the visuals. One thing that irked me a bit was you kept saying it's one-dimensional. A plane has 2 dimensions, not one. You can't draw a parabola with only one dimension. Maybe you meant to say that the function is univariate.

[luisalcaraz]

Where have you been my whole math career!!!! Thank you for the videos

[aditidump]

can anyone tell me how to solve 8:28 the derivative at a direction other than x or y?