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Nov 2, 2012 at 15:13 comment added Gerald Edgar Yes. Note that even the muddled definition on the mathworld web site says that trigonometric functions are included among "elementary functions".
Nov 2, 2012 at 10:51 answer added juan timeline score: 2
Nov 2, 2012 at 10:49 comment added fedja That theorem relates to the "Hardy field" (See en.wikipedia.org/wiki/Hardy_field), not to elementary functions in the sense of Liouville. The latter have no such property: just take $f_1=x(2+\sin x)$ and $f_2=x$.
Nov 2, 2012 at 8:57 history asked user27381 CC BY-SA 3.0