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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)
 > $\mathrm{D}\left(⟨{x}^{2},{y}^{2},{z}^{2}⟩\right)$
 $\left({2}{}{\mathrm{D}}{}\left({x}\right){}{x}\right){{e}}_{{x}}{+}\left({2}{}{\mathrm{D}}{}\left({y}\right){}{y}\right){{e}}_{{y}}{+}\left({2}{}{\mathrm{D}}{}\left({z}\right){}{z}\right){{e}}_{{z}}$ (2)
 > $\mathrm{D}\left[2,1\right]\left(\left(x,y\right)↦⟨y\cdot {x}^{2}+{y}^{2}+3\cdot y\cdot x,{x}^{2}\cdot {y}^{3},y\cdot x⟩\right)\left(x,y\right)$
 $\left({2}{}{x}{+}{3}\right){{e}}_{{x}}{+}\left({6}{}{x}{}{{y}}^{{2}}\right){{e}}_{{y}}{+}\left({1}\right){{e}}_{{z}}$ (3)