The derivative of a function gives the rate of change of the function at a given point. If the function measured position over time (where x = increasing values of time and f(x) equals a measure of distance), the INSTANTANEOUS VELOCITY at a given point of the curve can be represented by the rate of change of distance with the respect to time. In other words, the same method to calculate the slope of a line tangent to a function at a given point can be used to calculate velocity for functions involving the change of distance over time.
The only thing different about these functions is that the independent variable is 't' (as opposed to 'x'), with the dependent variable being 's' (as opposed to 'y').
Find the instantaneous velocity at t = 3 for the function: $s\left(t\right)=\frac{1}{t+2}$
Derivative and velocity.