Definition:Differential of Mapping/Notation

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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:

$\d y = \dfrac {\d y} {\d x} \rd x$


Sources