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user583825
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What is the necessary and sufficient condition for a chain rule hold?
I found the result. Thie result is an easy consequence of Theorem 3.59 in the book ``A first course in Sobolev spaces: Second Edition", Print ISBN: 978-1-4704-2921-8.
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What is the necessary and sufficient condition for a chain rule hold?
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What is the necessary and sufficient condition for a chain rule hold?
Yes, the chain rule holds for $[c, +\infty)$ for any $c>0$, but how to handle the derivative near the origin? Is it still holds for the origin? @fedja
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What is the necessary and sufficient condition for a chain rule hold?
Well, $f$ is $C^1$ means that $f \in C^1((0, +\infty))$. @fedja
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What is the necessary and sufficient condition for a chain rule hold?