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

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The discussion revolves around proving the equation dx/dy * dy/dz * dz/dx = -1 using partial derivatives and the chain rule. The original poster struggles with the problem due to a lack of complete information about the function involved. Participants suggest that implicit differentiation is necessary, assuming f(x,y,z)=0 defines x, y, and z as functions of each other. The importance of correctly applying the chain rule and the rules of partial derivatives is emphasized. The conversation highlights the need for clarity in problem statements for effective problem-solving in calculus.
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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