Suppose $A$ and $B$ are both open sets, and there is a diffeomorphism $g$ between them. My book says that the chain rule implies that $Dg$ is non-singular. I don't understand. Can anyone tell my why?
2026-04-03 07:43:02.1775202182
something about diffeomorphism
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I figured it out myself. Actually we notice composite of g and g inverse is identity. Using chain rule on composite of g and g inverse we can get the conclusion.