The line element in terms of the metric tensor, \(q_{\alpha \beta}\) is given by

\[d s^{2}=g_{\alpha \beta} d x^{\alpha} d x^{\beta}\]

Show that the transformed metric for the transformation \(x^{\prime \alpha}=x^{\prime \alpha}\left(x^{\beta}\right)\) is given by

\[g_{\gamma \delta}^{\prime}=g_{\alpha \beta} \frac{\partial x^{\alpha}}{\partial x^{\prime} \gamma} \frac{\partial x^{\beta}}{\partial x^{\prime \delta}}\]