If u= (x^3+y^3+z^3-3 x y z ), then (x+y+z) (u_x+u_y+u_z ) is equal to

Step-by-step solution

Given, u= (x^3+y^3+z^3-3 x y z ) aligned & u_x= d u d x = 3 x^2-3 y z (x^3+y^3+z^3-3 x y z ) & u_y= d u d y = 3 y^2-3 x z x^3+y^3+z^3-3 x y z aligned and u_z= d u d z = 3 z^2-3 x y x^3+y^3+z^3-3 x y z aligned & u_x+u_y+u_z & = 3 (x^2+y^2+z^2-x y-y z-z x ) (x+y+z) (x^2+y^2+z^2-x y-y z-z x ) & (x+y+z) (u_x+u_y+u_z )=3 aligned