Definition:Differential of Mapping/Notation

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


 * $\map {\d f} x$
 * $\d f_x$
 * $\d_x f$
 * $\map {D f} x$
 * $D_x f$

Substituting $\d y$ for $\map {\d f} {x; h}$ and $\d x$ for $h$, the following notation emerges:
 * $\d y = \map {f'} x \rd x$

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