facenian
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Helo, given ##f:R^n\rightarrow R^m## and ##g:R^m\rightarrow R^e## both class ##C^m##. Is the composition ##g\circ f## of class ##C^m## ?.
Elementary question on composition of functions
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Yes, use the chain rule to prove it.
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BTW, I believe this exercise appears in Munkres Analysis on Manifolds with a suitable guidance, but I am not 100% sure.
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