$\frac{\delta f(x)}{\delta x}$ seems to be a totally abused notation whenever an author (usually in control theory or thermodynamics or some engineering discipline) decides to quantify "slight variation"
More frustrating is that attempt results $\frac{\delta f(x)}{\delta x}$ being the same as $\frac{df(x)}{d x}$, something we know and love dearly.
Under what context can we use $\frac{\delta f(x)}{\delta x}$ to characterize variation (i.e. is there some rigorous definition that utilize this notation)? and is there ANY different between this and the regular notation for derivative?