Partial Derivatives: Show ∂f/∂x+∂f/∂y+∂f/∂z=0

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SUMMARY

The discussion centers on proving the equation ∂f/∂x + ∂f/∂y + ∂f/∂z = 0 for a differentiable function f(u, v, w) where u = x - y, v = y - z, and w = z - x. The chain rule for partial derivatives is essential for this proof, specifically using the formula (df/dx) = (df/du)(du/dx) + (df/dv)(dv/dx) + (df/dw)(dw/dx). Participants express confusion regarding the application of these concepts, indicating a need for clearer understanding of partial derivatives and the chain rule.

PREREQUISITES
  • Understanding of partial derivatives
  • Familiarity with the chain rule in calculus
  • Knowledge of differentiable functions
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the application of the chain rule for partial derivatives in multivariable calculus
  • Explore examples of differentiable functions and their partial derivatives
  • Learn about the implications of the equation ∂f/∂x + ∂f/∂y + ∂f/∂z = 0 in vector calculus
  • Practice solving problems involving transformations of variables in multivariable functions
USEFUL FOR

Students studying multivariable calculus, educators teaching calculus concepts, and anyone seeking to deepen their understanding of partial derivatives and their applications.

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Homework Statement



If f(u, v, w) is differentiable and u=x-y, v=y-z, and w=z-x, show that

∂f/∂x+∂f/∂y+∂f/∂z=0

Homework Equations



I am completely lost.:cry:

The Attempt at a Solution



I am completely lost. :cry:
 
Physics news on Phys.org
Chain rule for partial derivatives. E.g. (df/dx)=(df/du)(du/dx)+(df/dv)(dv/dx)+(df/dw)(dw/dx) (all derivatives partial).
 

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