What are some practical applications of successive differentiation?

Before starting to learn something, I always wonder whats its application. So would you please give some practical examples of application of Successive differentiation and concepts related to it such as Taylor's series?

Any time you need a higher derivative, you have to get there through successive differentiation. For example, if $$s(t)$$ is the position of a particle at time $$t$$, then $$\frac{d^3s(t)}{dt^3}$$ is the "jerk". To get it, you have to compute $$\frac{ds(t)}{dt}$$, $$\frac{d^2s(t)}{dt^2}$$, and then $$\frac{d^3s(t)}{dt^3}$$.