What are derivatives in 3D? Intro to Partial Derivatives
ฝัง
- เผยแพร่เมื่อ 3 ก.ค. 2024
- 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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Thank you so much for this playlist. It helped me get intuition on my multivariable calculus course
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Ugh!!!!!!! Where have you been my whole math career!!!! Thank you for the videos
Amazing work!!! Hope to see you coming with more videos :D
I love watching this out of pure interest while still taking my high school AP calculus BC course!
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!
th-cam.com/video/XQIbn27dOjE/w-d-xo.html 💐
Very clear and concise
The audio was a bit weird at times. Also nice work on the graphics.
Excellent explanation
Nice work on the Graphics part sir. Thank you so much for this video. ❤️ From 🇮🇳
Really thanks, it was hard to get the big picture of these subjects by studying from a book.
really fantastic quality videos - great job
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great explanation! thank you so much!
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Keep up the good work sir 👏
Superb!!
Great video!!
Thank you sir 🔥🔥🔥
Wow! Thank you so much.
U r voice,animation everything is amazing
Thank you!
You are my hero
Great explanation
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helping the algorithm work for my MAN's benefit
love it:D
thank you
mathmagician !
I ploted the equations on a 3D plot and the differention made meaning graphically as a tangent to the function.
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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.🙏🙏🙏🙏😇😇😇😇❤️❤️❤️❤️❤️
haha technical difficulties on this one:D
Not me binging this playlist 2 days before my calc 3 exam
good explaination
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Love u sir
thanks
Doctor, I ask you to download a video that shows how to find the derivative of two variables of functions using the definition
If I understood linear algebra right, at 1:39 Shouldnt it be f(x0,z0)? basically hyperplane y0 chops it out thats the constraint/constant for y. Which will leave z remaining. So the function should have z in them. Right?
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.
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.
Thanks! My main camera died on this one hence no visual of me and bad audio, should be a one time thing:)
How do you make such a nice visualization? I mean the 3d with cut shape.
You could make a partial derivative video on the youtube algorithmn! haha
What's the partial derivative of youtube recommendation function with respect to likes / subscriber count / comments / length of video watched.
I guess the output would be the total # of people recommended the video out of the total population.
I have no clue how you would actually get the data though, but it would be a fun example to just make up data
What about the gradient vector, how does it look?
I actually have a whole video on this in the calculus III playlist, check it out:)
What books will you recommend for Calculas? , your's fan !
Google "Active Calculus" - it's totally free and has calc 1-3
@@DrTrefor Thank you , sir
sound was less and we need ur face explaining bt alll awesome
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.
There is a distinction between the dimension of the object itself, and the space in which it lives. So if you take your example of a parabola, this is a "one dimensional curve" that is embedded or living within two dimensions. That is, there is one degree of freedom. The term univariate I see what you mean as well, it isn't typically the word that is used here (has a bit more of a statistics flare to it) but you are meaning the same idea.
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Y not here denotes it is at a fixed point in y
awesome visuals, just wish you had a better mic :(
I’ve since bought one haha! Actually it was mostly changing rooms that was crucial
Why isn't the surface a function of x,y and z. Why only x,y?
Sound isn't clear
Which software you use ?
Trefor Bazett can you provide me some resources where I can learn to animate ? Or if you can make a course where you teach us these techniques ? This helps me very much to grasp the concepts.
th-cam.com/video/XQIbn27dOjE/w-d-xo.html 💐
and how the second derivative will be in 3d? like fxx and fxy for example?
Same sort of idea as from 2D, it's a measure of concavity in those particular directions
@@DrTrefor i thought that it will be something like that but I couldn’t figure out the difference between fxx and fxy
@@alibader910 do tell me once you get it?
What is Y naugth ?
It is just short-hand for a constant. It is some constant.
sir t$awed
like
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
WHY ARE WE YELLING!!!?!?
only if u were a girl 😂
@@MrGarg10may 😁
@@elimarburger1659 SOME HOW THE CAPS LOCK GET ON LIKE THIS TIME...
@@shubhamsatyaprakash54 OOOF
good lecture but audio quality is bad, pitch changes and too much high tones.
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@@beoptimistic5853 this video opened my eyes to a whole new world. others plz dont watch this
Why are you ignoring z axis in all this? The parabola looks like a function of z and x axis...since y is fixed
The idea is z is the output. I.e. z=f(x,y) and if y is fixed then just z=f(x)
Great video!