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QUESTION

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.

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.

:−ℎ ( , , ) ℎ ==> − , = − = 1, + + = = + + =− + = −1 = 0, = (1), (2) =0 = 1, = −1 , + = − = −1 , = 0, = , + =1 +0−+0+ = 0− + − +0+ … … … … … … … (1)...
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