$$ \overrightarrow {F}=3xz^{2}i+2xyj-x^{2}k $$ $$\phi =3x^{2}-yz $$ are given vector and scalar fields, respectively.
a) $\quad \operatorname{div}\left( \operatorname{grad}\phi \operatorname{div}\overrightarrow {F}\right) =\quad? $
b) $\quad \operatorname{curl}\left( \phi F\right) =\quad? $
c) $\quad \operatorname{div}\left( \phi F\right) =\quad? $
d) $\quad \overrightarrow {\nabla }\cdot \left( \nabla \phi \times \overrightarrow {F}\right) =\quad? $
e) $\quad \nabla \cdot \left( \overrightarrow {F}\nabla \phi \right) =\quad? $
I know the operations such as the Gradient, Divergence, Curl, and Laplacian. But I don't have an idea what can I do in this kind of problems?
