Derivative of a position vector valued function | Multivariable Calculus | Khan Academy

Visualizing the derivative of a position vector valued function

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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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[badlydrawnturtle]

"Instantaneous change"
You hear distant screaming from the direction of 3B1B...

[aidan]

I might be late, but I feel it's important to note that the derivative of the position vector r(t) being the derivatives of the scalar functions of its components only works in this case due to i_hat and j_hat being constant. Note that the components are actually scalar functions multiplying the unit vectors, so the product rule must be used, so you would actually get two terms for the derivate of x and two terms for the derivate of y, however as the unit vectors are constant their derivatives are 0 so you are left with this nice derivative. But remember, it only works due to the constant unit vectors, so would be different in polar coordinates etc :)

[lawrencemwangi]

From Kenya and I really appreciate this.

[aishikbhattacharya]

I have never come across with a teacher with such depth concepts in multivariable calculas..!!

[FBWUniverseMode]

We were studying normally, until this appeared on the board, the teacher never explained all this, and we were like tf?

[arahman]

You save my life many times. @khan academy

[meeralakshmis]

can u plz explain LIMIT AND CONTINUITY of a vector valued fn? coz i couldnt find a video on d same

[pirsbarker]

sal's voice is like of an angel to me

[RoyalYoutube_PRO]

one thing that I didn't understand that I now do... as opposed to parametric functions which had 2 inputs to 1 output, this one has one input and 2 outputs... (should have been obvious)

[latestjobsupdates]

I think r is not a function. it can not have two values of y for one value of x.
Correct me if I am wrong.

[REXATERPANTHERA]

"hand wavy" It's been too long Sal, good to hear that again.

[pietergeerkens]

I'm concerned that I cannot tell if you're using dx, dy, dt or ∂x, ∂y, ∂t.
Isn't that distinction supposed to be rather critical in multi-variable calculus?

[jisyang]

at 12:02 you misspoke. vertical, not horizontal unit vector.

[ManojKumar-cjoj]

Scaler valued function vs vector valued function

[NGBigfield]

Every time he talks about colors, I lough.
I have no idea why

[JEHAD]

It is called PURPLE colour for ordinary people :-D

[zes]

no such thing as respec or not about it, nonex

[Dziaji]

Oh no. I really wanted to watch this video presented by Grant, and in the first 5 seconds, i had to shut this video off because this guy has the most obnoxious tone combined with the worst overdriven mic I can imagine. Please get Grant to redo this video.