Vector valued function derivative example | Multivariable Calculus | Khan Academy

Concrete example of the derivative of a vector valued function to better understand what it means

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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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[deziiiii]

i always follow your teaching only. u are the best online sir for me at least. thx and very great explanation. thx sir

[altuber_athlete]

So, summarising what we've seen in these few last videos: the magnitude of the derivative of vector function that represents the position of particle in time, with reapect to time, is the speed of the particle at each time _t, _ and therefore since the position of the particle at each point is represented by the curve, then the speed is at a spefic time _t, _ meaning the velocity (the vector corresponding to that speed) at that time is tangent to the curve.

[BoZhaoengineering]

This comparison is awesome . My mind is blowing. I have not notice the difference between the two vector functions before.

[dchangebegins]

Thank you..the best part of ur videos is it helps to shape the way we approach towards the sum.

[earendilthebright]

Excuse me good Sir/Madame, do you have a moment to hear the word of Sal?

[HoshinoMirai]

Thanks so much, Khan! You are the best!

[norwayte]

Great. Great. Great. - And thanks for the parameterization review.

[abdulhamidalsalman]

Very Nice. Great teaching Ideas. Thanks a lot

[cauchyschwarz]

What bugs me a little is that these derivative vectors are often drawn at the position where the derivative is taken. But the derivative vector you calculate would start at the origin. So what you display is f(t)+f'(t).