# Derivative and differential

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.

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