Is there any diference between derivative and differential? I was reading Peter Olver`s Applications of Lie groups to differential equations and in the first chapter ( pages 32 and 33 ) I could find the expressions DERIVATION and DIFFERENTIAL with some difference between their definitions. After reading this, I am asking myself if I really know what a derivative is.

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    $\begingroup$ Same thing, packed slightly differently. Say for $f:\mathbb R\to\mathbb R$, $df=f'(x)dx$. $\endgroup$ – Gil Bor Mar 9 '14 at 5:38

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