4-Vectors—Tensors

In the LCF \(\Sigma \) the vector field \(A^{i}\) has components \(A^{i}=\left( \begin{array}{c} e^{xc}\\ xe^{x}\\ 0\\ x \end{array} \right) _{\Sigma }.\) Compute the divergence \(A_{,i}^{i}\) in the LCF \(\Sigma ^{\prime }\) which moves wrt \(\Sigma \) with velocity \(\textbf{u}=kc{\hat{\textbf{x}}}\) \(({k<1})\) .