nder[n_,m_,f_]:=Derivative[Flatten[nvec[n,m]]][f]​​nvec[n_,m_]:=Table[If[in,1,0],{i,1,m}]
ff=Function[{x,y,z},x^2+y^2+z^2+xy-yz+3xz]
Function[{x,y,z},
2
x
+
2
y
+
2
z
+xy-yz+3xz]
nder[2,3,ff]
Function::fpct:Too many parameters in {x,y,z} to be filled from Function{x,y,z},
2
x
+
2
y
+
2
z
+xy-yz+3xz[{#1,#2,#3}].

({0,1,0})
Function[{x,y,z},
2
x
+
2
y
+
2
z
+xy-yz+3xz]