Two identical questions are here:
A question about differential forms
and here:
http://mathforum.org/kb/thread.jspa?forumID=13&threadID=2141549&messageID=7208112
In his proof, Rudin says that $\gamma$ is "clearly" $C^1$, which I found a bit confusing. Each $F_i$ was $C^1$ as proved, why is it clear that $\gamma$ is also $C^1$? Doesn't it require each $F_i$ to be $C^2$ in order for the partial derivatives to be $C^1$?
The problem is on the bottom of page 279 of Principles of Mathematical Analysis.
Rudin's Original Text Shot:
