Achar divergência e rotacional

[franufscar]

Sejam Ф(x,y,z) = x²yz³
F(x,y,z) = xy i - y² j + 2x²y k

Calcular: div(ФF) e rot(ФF)

[João P. Ferreira]

Divergência

\(\operatorname{div}\,\mathbf{F} = \nabla\cdot\mathbf{F}=\frac{\partial F_1}{\partial x_1}+\frac{\partial F_2}{\partial x_2}+\cdots +\frac{\partial F_n}{\partial x_n}\)

Rotacional

\(\nabla \times F(x,y,z) = \begin{bmatrix}
{\frac{\partial F_z}{\partial y}} - {\frac{\partial F_y}{\partial z}} \\ \\
{\frac{\partial F_x}{\partial z}} - {\frac{\partial F_z}{\partial x}}\\ \\
{\frac{\partial F_y}{\partial x}} - {\frac{\partial F_x}{\partial y}}
\end{bmatrix}\)

considerando
Ф(x,y,z) = x²yz³
V(x,y,z) = xy i - y² j + 2x²y k

no seu caso \(F=\Phi(V)=(xy)^2.y^2.(2x^2.y)^3\)