\begin{pmatrix}     \dfrac{\partial f_0}{\partial x}(g_0(z), g_0(z), z) & \dfrac{\partial f_0}{\partial y}(g_0(z), g_0(z), z)\\ \dfrac{\partial f_0}{\partial x}(g_0(z), g_0(z), z) & \dfrac{\partial f_0}{\partial y}(g_0(z), g_0(z), z)