Am I right that I can write/interpret any derivative $\frac{\partial f(x)}{\partial x}$ as derivative around zero, i.e.:
$\frac{\partial f(x)}{\partial x}=\left.\frac{\partial f(h+x)}{\partial h}\right|_{h=0}~?$
Is this interpretation/notation in any way common?
I am asking this basic question since I am trying to look at the Euclidean space as a special case of a (Lie) manifold.