Ex$.4.$ If $u=lo{g}_e(x^3+y^3+z^3-3xyz),$ prove that

$($b$)(\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{x}}+\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{y}}+\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{z}}{)}^{2}u=-\frac{9}{(x+y+z{)}^2}$;

$($c$)\frac{de{l}^{2}u}{del{x}^2}+\frac{de{l}^{2}u}{del{y}^2}+\frac{de{l}^{2}u}{del{z}^2}=-\frac{3}{(x+y+z{)}^2}.$

Please explain each and every step.