Formula_4809

\[[f, g]=f \frac{\partial g}{\partial z}-\frac{\partial f}{\partial z} g-x\left(\frac{\partial f}{\partial x} \frac{\partial g}{\partial z}-\frac{\partial f}{\partial z} \frac{\partial g}{\partial x}\right)-\frac{\partial f}{\partial x} \frac{\partial g}{\partial y}+\frac{\partial f}{\partial y} \frac{\partial g}{\partial x} .\]