please scroll down to "Proof of The Chain Rule" & " Alternative Proof of the Chain Rule" in this website and leave your comment and answer to the question(is it bogus?)(be serious!):
http://www.karlscalculus.org/calc4_3.htm…
http://www.karlscalculus.org/calc4_3.htm…
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This part looks bogus: "in the limit, g(x + h) = g(x) + (h g'(x) )"
It means the limit as h->0 so basically this statement says g(x) = g(x), which definitely isn't helpful in proving the chain rule. So that is not good logic.
This does seem to suggest a good proof, which can be established through the mean value theorem I think. But as it is written, it is bogus.
It means the limit as h->0 so basically this statement says g(x) = g(x), which definitely isn't helpful in proving the chain rule. So that is not good logic.
This does seem to suggest a good proof, which can be established through the mean value theorem I think. But as it is written, it is bogus.