A vector calculus proof question

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Homework Help Overview

The discussion revolves around a vector calculus proof question involving the total derivative and the dot product of the gradient of a scalar function with a differential vector. Participants express uncertainty about the initial steps and the provided hint.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the gradient and the total derivative, with some attempting to clarify how to express the gradient in terms of unit vectors. Questions arise regarding the interpretation of the hint and the initial steps needed to approach the problem.

Discussion Status

Some participants have offered guidance on expressing the gradient and the differential vector, while others are still seeking clarity on the first steps. There is a sense of collaboration as participants share their understanding and interpretations, though no consensus has been reached.

Contextual Notes

Participants note that the problem is new to them, and there is mention of a hint that is not fully understood. The discussion reflects a learning environment where assumptions and interpretations are being examined.

physics2000
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Homework Statement



The image contains the problem statement and all relevant equations. I have no idea what to do, this is all very new to me...plus the hint doesn't make sense to me.

[url=http://postimage.org/][PLAIN]http://s13.postimage.org/b0kq27bkn/photo_6.jpg[/url] photo uploader[/PLAIN]
 
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physics2000 said:

Homework Statement



The image contains the problem statement and all relevant equations. I have no idea what to do, this is all very new to me...plus the hint doesn't make sense to me.

[url=http://postimage.org/][PLAIN]http://s13.postimage.org/b0kq27bkn/photo_6.jpg[/url] photo uploader[/PLAIN]

I think they just want you to show that the dot product of grad(∅) with dr gives you the expression for d(∅) in the expression for the total derivative in the hint.
 
I kind of understand what you mean, but not sure what the first step is:confused:
 
physics2000 said:
I kind of understand what you mean, but not sure what the first step is:confused:

You've got dr in terms of the unit vectors with the hats on them. Write out grad(phi) in terms of the unit vectors and take the dot product.
 
Dick said:
You've got dr in terms of the unit vectors with the hats on them. Write out grad(phi) in terms of the unit vectors and take the dot product.

is this what you mean?... i think I was overthinking it , thanks for your help!

[url=http://postimage.org/][PLAIN]http://s2.postimage.org/rgazdfeih/photo_7.jpg[/url] online photo storage[/PLAIN]
 
Yes, I think that's what they want.
 

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