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?