In my lecture notes for Lie groups, it has the following line for calculating the tangent map for left-translation $L_g (x) = gx$ on an n-dimensional matrix lie group of $d \times d$ matrices.
$$(gx)_\mu ^\nu = g_\mu ^\tau x_\tau ^\nu \implies (T_xL_g)_{\mu \sigma}^{\nu \rho} = \frac{\partial (gx)_\mu^\nu}{\partial x_\rho^\sigma} = g_\mu^\tau \delta_\tau^\rho \delta_\sigma^\nu = g_\mu^\rho \delta_\sigma^\nu$$
My confusion is with the following equality: $$ (T_xL_g)_{\mu \sigma}^{\nu \rho} = \frac{\partial (gx)_\mu^\nu}{\partial x_\rho^\sigma} $$
Where does this come from?