f=(1/C*(#1+(#2^2+#3^2)/2))^(1/(γ-1)) &

U = {(1/C*(#1+(#2^2+#3^2)/2))^(1/(γ-1)),(1/C*(#1+(#2^2+#3^2)/2))^(1/(γ-1))*#2,(1/C*(#1+(#2^2+#3^2)/2))^(1/(γ-1))*#3}&

F= {#3*(1/C*(#1+(#2^2+#3^2)/2))^(1/(γ-1)),#3*(1/C*(#1+(#2^2+#3^2)/2))^(1/(γ-1))*#2,#3*(1/C*(#1+(#2^2+#3^2)/2))^(1/(γ-1))*#3+C*(1/C*(#1+(#2^2+#3^2)/2))^(γ/(γ-1))}&

A=Transpose[FullSimplify[{ D[F[V1,V2,V3],V1], D[F[V1,V2,V3],V2],  D[F[V1,V2,V3],V3]}]]