In physics, it is common to define the horizontal position $x$ and the vertical position $y$ of an object as functions of $t$ and then us the formula $$\dfrac {dy}{dx}=\dfrac {\dfrac {dy}{dt}}{\dfrac {dx}{dt}}$$ to determine the velocity of the object (which is the same as its instantaneous rate of change).
Suppose one is working with a parametric function that defines the position of an object in $\mathbb{R} ^{3}$ as $$x=f\left( t\right)$$ $$y=g\left( t\right)$$ $$z=h\left( t\right)$$ where $f$, $g$, and $h$ are continuous functions.
What formula could one use in order to determine the rate of change of the parametric, or the velocity of that object? What is that formula called? In what ways does the process relate to total and partial derivatives?