most recent 30 from http://mathoverflow.net 2013-05-26T09:43:18Z http://mathoverflow.net/feeds/user/10557 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/44774/do-these-properties-characterize-differentiation/44783#44783 Pedro Solorzano 2010-11-04T05:47:34Z 2010-11-04T05:47:34Z

<p>I remember thinking the same thing as Richard is saying and thinking about defining $L$ simply by using the third property. I believe only using this property you can prove change rule (but maybe I'm wrong, and my notes are far away). </p> <p>The caveat is that if you don't use $L(x)=1$, then you can think of (with suitable restrictions on domains) the following: </p> <p>$$L(f)(x)=\frac{f(x)}{x}$$</p> <p>which, by the way, satisfies the chain rule. :)</p>