Oblicz dywergencję funkcji [latex]sin^3(r^2)overrightarrow{r}[/latex], gdzie [latex]overrightarrow{r}[/latex] = (x,y,z), a r = [latex]sqrt[(x^2+y^2+z^2)][/latex]

F1(xyz)=x·sin³(x²+y²+z²) F2(xyz)=y·sin³(x²+y²+z²) F3(xyz)=z·sin³(x²+y²+z²) [latex]div(F)=frac{partial F_1}{partial x}+frac{partial F_2}{partial y}+frac{partial F_3}{partial z}[/latex] [latex]=sin^3(x^2+y^2+z^2)+6x^2cdot sin^2(x^2+y^2+z^2)cdot cos(x^2+y^2+z^2)+[/latex] [latex]sin^3(x^2+y^2+z^2)+6y^2cdot sin^2(x^2+y^2+z^2)cdot cos(x^2+y^2+z^2)+[/latex] [latex]sin^3(x^2+y^2+z^2)+6z^2cdot sin^2(x^2+y^2+z^2)cdot cos(x^2+y^2+z^2)+[/latex]