Question: Consider the function z(x, y), its partial derivatives (z/x)y and (z/y)x, and the total derivative dz/dx. (a) How do the magnitudes (x)y and dx compare?

Consider the function z(x, y), its partial derivatives (∂z/∂x)y and (∂z/∂y)x, and the total derivative dz/dx.
(a) How do the magnitudes (∂x)y and dx compare?
(b) How do the magnitudes (∂z)y and dz compare?
(c) Is there any relation among dz, (∂z)x, and (∂z)y?

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