Total Derivative

In multivariable functions $f (x_{1} (t), x_{2} (t) \dots x_{n} (t), t)$ , the total derivative $\frac{d f}{d t}$ with respect to one of the variables (t here) is:

\frac{d f}{d t} = \frac{\partial f}{\partial x_{1}} \frac{d x_{1}}{d t} + \frac{\partial f}{\partial x_{2}} \frac{d x_{2}}{d t} + \dots + \frac{\partial f}{\partial x_{n}} \frac{d x_{n}}{d t} + \frac{\partial f}{\partial t}