Module[{fa,fb,fc},fa[{x_,y_,z_}]:=z;fb[{x_,y_,z_}]:=;fc[{x_,y_,z_}]:=Cos[y];Simplify[With[{v={2,-1,3},p={2,0,-1}},{{"a",D[fa[p+tv],t]},{"b",D[fb[p+tv],t]},{"c",D[fc[p+tv],t]}}/.t->0]]]
2
y
7
x
x
SimplifyWith{v={2,-1,3},p={2,0,-1},fa=z,fb=,fc=Cos[y]},"a",v.fa,"b",v.fb,"c",v.fc,"c",fc
2
y
7
x
x
∇
{x,y,z}
∇
{x,y,z}
∇
{x,y,z}
∇
{x,y,z}