SCalcET$816\mathrm{.}5\mathrm{.}029.$

Iffis a scalar field andF,Gare vector fields, thenf$$F$,$F$$G$,$ andF$$Gare defined by

$($f$$F$)($x$,$ y$,$ z$)=$f$($x$,$ y$,$ z$)$ F$($x$,$ y$,$ z$)($F $$ G$)($x$,$ y$,$ z$)=$F$($x$,$ y$,$ z$)$ G$($x$,$ y$,$ z$)($F $$ G$)($x$,$ y$,$ z$)=$F$($x$,$ y$,$ z$)$ G$($x$,$ y$,$ z$).$

Find an identical expression, assuming that the appropriate partial derivatives exist and are continuous.

curl$($curl F$)$

div F $+$Fgrad$($div F$)$F$$grad$($curl F$)+2$Fgrad$($div F$)2$Fnone of the above