[tex] \text{div } \vec{F} = \nabla \: . \: \vec{F} \\ \\ \text{div } \vec{F} = \left( \frac{ \partial}{ \partial x} , \frac{ \partial}{ \partial y} , \frac{ \partial}{ \partial z} \right) \: \cdot \: (y {}^{2} z {}^{2} , \: z {}^{2} \sin (y) , \: x {}^{2} e {}^{y} ) \\ \\ \text{div } \vec{F} = \left( \frac{ \partial \: y {}^{2} z {}^{2} }{ \partial x} , \frac{ \partial z {}^{2} \sin(y) }{ \partial y} , \frac{ \partial x {}^{2} e {}^{y} }{ \partial z} \right) \\ \\ \text{div } \vec{F} =0 + z {}^{2} . \cos(y) + 0 \\ \\ \boxed{\text{div } \vec{F} = z {}^{2} . \cos(y)}[/tex]