Functions to Initialize

  
  grad2[f_]:={D[f[#1,#2],#1],D[f[#1,#2],#2]}&
  

  
  grad3[f_]:={D[f[#1,#2,#3],x],D[f[#1,#2,#3],#2],D[f[#1,#2,#3],#3]}&
  

  
  norm2[x_]:=Sqrt[x[[1]]^2+x[[2]]^2]
  

  
  norm3[x_]:=Sqrt[x[[1]]^2+x[[2]]^2+x[[3]]^2]
  

Up to Some Multivariable Calculus Ideas