diff - Maple Help

Student[VectorCalculus]

 diff
 compute the derivative of a Vector-valued function

 Calling Sequence diff(f, v)

Parameters

 f - Vector or algebraic expression v - name or name, name, ...; specify the variables of differentiation

Description

 • The diff(f, v) calling sequence is an extension of the top-level diff that performs coordinate-wise differentiation on Vectors (including vector fields), in the coordinate systems of the Student[VectorCalculus] package.  If f is not a Vector, the arguments are passed to the top-level diff command.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{VectorCalculus}\right]\right):$
 > $\mathrm{diff}\left(⟨t,{t}^{2},{t}^{3}⟩,t\right)$
 $\left({1}\right){{e}}_{{x}}{+}\left({2}{}{t}\right){{e}}_{{y}}{+}\left({3}{}{{t}}^{{2}}\right){{e}}_{{z}}$ (1)
 > $\mathrm{diff}\left(⟨\mathrm{cos}\left(st\right),\mathrm{sin}\left(st\right)⟩,s,t\right)$
 $\left({-}{\mathrm{sin}}{}\left({s}{}{t}\right){-}{t}{}{s}{}{\mathrm{cos}}{}\left({s}{}{t}\right)\right){{e}}_{{x}}{+}\left({\mathrm{cos}}{}\left({s}{}{t}\right){-}{t}{}{s}{}{\mathrm{sin}}{}\left({s}{}{t}\right)\right){{e}}_{{y}}$ (2)
 > $\mathrm{SetCoordinates}\left(\mathrm{spherical}\left[r,\mathrm{\phi },\mathrm{\theta }\right]\right)$
 ${{\mathrm{spherical}}}_{{r}{,}{\mathrm{\phi }}{,}{\mathrm{\theta }}}$ (3)
 > $F≔\mathrm{VectorField}\left(⟨ar,0,0⟩\right)$
 ${F}{≔}\left({a}{}{r}\right){\stackrel{{_}}{{e}}}_{{r}}{+}\left({0}\right){\stackrel{{_}}{{e}}}_{{\mathrm{φ}}}{+}\left({0}\right){\stackrel{{_}}{{e}}}_{{\mathrm{θ}}}$ (4)
 > $\mathrm{diff}\left(F,\mathrm{\phi }\right)$
 $\left({a}{}{r}{}{\mathrm{cos}}{}\left({\mathrm{\phi }}\right){}{{\mathrm{cos}}{}\left({\mathrm{\theta }}\right)}^{{2}}{}{\mathrm{sin}}{}\left({\mathrm{\phi }}\right){+}{a}{}{r}{}{\mathrm{cos}}{}\left({\mathrm{\phi }}\right){}{{\mathrm{sin}}{}\left({\mathrm{\theta }}\right)}^{{2}}{}{\mathrm{sin}}{}\left({\mathrm{\phi }}\right){-}{a}{}{r}{}{\mathrm{sin}}{}\left({\mathrm{\phi }}\right){}{\mathrm{cos}}{}\left({\mathrm{\phi }}\right)\right){\stackrel{{_}}{{e}}}_{{r}}{+}\left({a}{}{r}{}{{\mathrm{cos}}{}\left({\mathrm{\phi }}\right)}^{{2}}{}{{\mathrm{cos}}{}\left({\mathrm{\theta }}\right)}^{{2}}{+}{a}{}{r}{}{{\mathrm{cos}}{}\left({\mathrm{\phi }}\right)}^{{2}}{}{{\mathrm{sin}}{}\left({\mathrm{\theta }}\right)}^{{2}}{+}{a}{}{r}{}{{\mathrm{sin}}{}\left({\mathrm{\phi }}\right)}^{{2}}\right){\stackrel{{_}}{{e}}}_{{\mathrm{φ}}}{+}\left({0}\right){\stackrel{{_}}{{e}}}_{{\mathrm{θ}}}$ (5)
 > $\mathrm{diff}\left(F,a\right)$
 $\left({r}\right){\stackrel{{_}}{{e}}}_{{r}}{+}\left({0}\right){\stackrel{{_}}{{e}}}_{{\mathrm{φ}}}{+}\left({0}\right){\stackrel{{_}}{{e}}}_{{\mathrm{θ}}}$ (6)