\[f\]
is defined in terms of variables \[x_1, \l x_2,..., \; x_n\]
that are themselves functions of \[t\]
.
Then using the Differentiation - The Chain Rule we can write \[\frac{df}{dt}= \frac{dx_1}{dt}\frac{\partial f}{\partial x_1} + \frac{dx_2}{dt}\frac{\partial f}{\partial x_2} +...+ \frac{dx_n}{dt}\frac{\partial f}{\partial x_n} \]
.\[\frac{df}{dt}= \frac{dx_1}{dt}\frac{\partial }{\partial x_1} + \frac{dx_2}{dt}\frac{\partial }{\partial x_2} +...+ \frac{dx_n}{dt}\frac{\partial }{\partial x_n} \]
.Ising operatprs like this we can build an Operator Algebra.