Pregunta: a) If F=grad(x3+y3+z3−3xyz), find div F. 6) If A=3xz2−yz+(x+2z)k find curl(curlA).

To find $\mathrm{d}\mathrm{i}\mathrm{v}\overrightarrow{\mathrm{F}}$, we use the formula for the divergence in Cartesian coordinates

$\mathrm{d}\mathrm{i}\mathrm{v}\overrightarrow{\mathrm{F}}=\frac{\partial {\mathrm{F}}_{\mathrm{x}}}{\partial \mathrm{x}}+\frac{\partial {\mathrm{F}}_{\mathrm{y}}}{\partial \mathrm{y}}+\frac{\partial {\mathrm{F}}_{\mathrm{z}}}{\partial \mathrm{z}}$

Given $\overrightarrow{\mathrm{F}}=\mathrm{\nabla }({\mathrm{x}}^3+{\mathrm{y}}^3+{\mathrm{z}}^3-3\mathrm{x}\mathrm{y}\mathrm{z})$, we have