Proving Chain Rule for Partial Derivatives in Calculus 3 Extra Credit Problem

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Homework Help Overview

The discussion revolves around proving a relationship involving partial derivatives, specifically the equation dx/dy * dy/dz * dz/dx = -1. The context is within a calculus framework, particularly focusing on the chain rule and implicit differentiation.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the use of the chain rule and implicit differentiation. There are questions about the completeness of the problem statement and the assumptions necessary for the proof. Some participants discuss potential methods involving treating derivatives as quotients.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on the problem setup and the necessary assumptions. There is a suggestion to clarify the function involved in the problem, and some guidance on using implicit differentiation has been offered.

Contextual Notes

There is a noted lack of complete information regarding the function that defines the relationships between x, y, and z, which is essential for the proof. Participants are also considering the implications of assuming that f(x,y,z)=0 implicitly defines the variables.

ACLerok
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Hi I'm having trouble with this extra credit problem I've been given. I am supposed to prove:

dx/dy * dy/dz * dz/dx = -1 (partial derivatives)

I think I'm supposed to use the chain rule but not sure. Can anyone help me out?
 
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ACLerok said:
Hi I'm having trouble with this extra credit problem I've been given. I am supposed to prove:

dx/dy * dy/dz * dz/dx = -1 (partial derivatives)

I think I'm supposed to use the chain rule but not sure. Can anyone help me out?
This is not the complete statement of the problem. One has to know what the function is. Please provide the complete problem as given to you.

AM
 
sorry nope.. it's all i was given.
 
It's true in general. matt grime likes to bring it up now and then!

How did trying the chain rule go? (I assume you tried it, since you thought it would be a good idea) How did you set up the problem?
 
i figured if you treat them as quotients you can 'multiply' by dy/dx, dz/dy, and dx/dz to cancel them out but that wouldn't work.. I only said the chain rule cause my TA gave us that hint
 
firstly, it must be assumed f(x,y,z)=0 implicitly defines x as a function of y and z and y as a function of x and z and z as a function of x and y.

then just use the usual rules of implicit differentiation and partial derivatives.
 

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