Help with Vector Calculus Derivative

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Homework Help Overview

The discussion revolves around a vector calculus problem involving the derivative of the dot product of a vector function with itself. Participants are examining the expression for the derivative and the properties of the dot product that apply to this situation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the properties of the dot product to understand how the expression simplifies to a specific form. Questions are raised about the conditions necessary for the equality to hold and the fundamental properties that might apply.

Discussion Status

Some participants have identified relevant properties of the dot product that clarify the reasoning behind the expression. There is acknowledgment of the fundamental nature of these properties, indicating a productive exploration of the topic.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information they can share or the methods they can use to arrive at a solution.

rad0786
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Hey... i was hopeing somebody can help me with a homework question... its about vector calc... taking the deriviative.

d/dx[r(t) dot r(t)] = r'(t) dot r(t) + r(t) dot r'(t) = 2r'(t) dot r(t)

I know it sounds sillly, but i was just wondering how on Earth they got
2r'(t) dot r(t) ?
 
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Well, go through the list of properties of the dot product -- any of them look useful?
 
Another approach... what must be true for that last equality
r'(t) dot r(t) + r(t) dot r'(t) = 2r'(t) dot r(t)
to happen (assuming that each side is correct)?
This should lead to the property hinted by Hurkyl.
 
Okay i see it now.

It comes from the property...

a dot (b + c) = a dot b + a dot c

:)

Thanks for poinitng that out...
 
Ah, right -- that one's so fundamental I forgot it even needed to be invoked! (I had only noticed you needed a.b = b.a)
 

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