Calculus 3 extra credit

[ACLerok]

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?

[Andrew Mason]

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

[ACLerok]

sorry nope.. it's all i was given.

[Hurkyl]

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?

[ACLerok]

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

[matt grime]

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.