Definition:Differential of Mapping/Notation

Notation for Differential
There are various notations for the differential of a function $f$ at $x$:


 * $\rd f \left({x}\right)$
 * $\rd f_x$
 * $\rd_x f$
 * $D f \left({x}\right)$
 * $D_x f$

Substituting $\rd y$ for $\rd f \left({x; h}\right)$ and $\mathrm d x$ for $h$, the following notation emerges:
 * $\rd y = f' \left({x}\right) \rd x$

hence:
 * $\rd y = \dfrac {\rd y} {\rd x} \rd x$