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VectorCalculus

 D
 apply the differential operator to an expression

 Calling Sequence D(f) D[i](f)

Parameters

 f - 'Vector'(algebraic), Vector valued procedure or expression which can be applied as a function i - positive integer or expression or sequence of integers or expressions

Description

 • The D(f) command applies the differential operator to an expression.  The command extends the differential operator D to operate on Vectors and Vector valued procedures.

Examples

 > $\mathrm{with}\left(\mathrm{VectorCalculus}\right):$
 > $\mathrm{D}\left(\mathrm{sin}\right)$
 ${\mathrm{cos}}$ (1)
 > $\mathrm{D}\left(⟨{x}^{2},{y}^{2},{z}^{2}⟩\right)$
 ${2}{}{\mathrm{D}}{}\left({x}\right){}{x}{{e}}_{{x}}{+}{2}{}{\mathrm{D}}{}\left({y}\right){}{y}{{e}}_{{y}}{+}{2}{}{\mathrm{D}}{}\left({z}\right){}{z}{{e}}_{{z}}$ (2)
 > $\mathrm{D}[2,1]\left(\left(x,y\right)→⟨y{x}^{2}+{y}^{2}+3xy,{x}^{2}{y}^{3},xy⟩\right)\left(x,y\right)$
 $\left({2}{}{x}{+}{3}\right){{e}}_{{x}}{+}{6}{}{x}{}{{y}}^{{2}}{{e}}_{{y}}{+}{{e}}_{{z}}$ (3)