A doubt on total differentials

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    Differentials Doubt
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Homework Help Overview

The discussion revolves around the concept of total differentials in calculus, specifically in the context of a problem involving a horizontal plane and the identification of a rectangle within that plane.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the definition of total differentials and question the validity of a short proof regarding the relationship between partial derivatives and small changes in dimensions.

Discussion Status

The discussion is ongoing, with participants providing clarifications and definitions related to total differentials. There is an indication of productive engagement, as one participant acknowledges the need to improve clarity in their communication.

Contextual Notes

One participant notes the importance of clear communication in mathematical discussions, suggesting that typed statements may facilitate better feedback.

Rishabh Narula
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Please refer to the images and my handwritten note(i tried my best handwriting) for the question
 

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There is a horizontal plane (z constant) through the point P. They are identifying a rectangle in it as PDEF. There is nothing there that one can argue with. It is not "sloped". With that in mind, you should reconsider your thinking.

PS. If you type your statements in, then it is easier for people to comment on specific parts of it.
 
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Thanks,will do that next time onwards.Is the short proof right,that the different partials multiplied by small changes in different dimensions,when added up give the total small change?
 
That is what is defined as the "total differential".
 

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