  Observer-invariance is regarded as a minimum requirement for an appropriate
definition and derived systematically from a spacetime setting, where
observer-invariance is a special case of a covariance principle and covered by
Ricci-calculus. The analysis is considered for tangential n-tensor fields on
moving surfaces and provides formulations which are applicable for
computations. For various special cases, e.g., vector fields (n = 1) and
symmetric and trace-less tensor fields (n = 2) we compare material and
convected derivatives and demonstrate the different underlying physics.
