The process of finding derivatives can be done beyond the first derivative. The derivative of f(x) is called the 1st derivative. This is also the velocity function of f(x). The derivative of the 1st derivative is the 2nd Derivative. This is called the acceleration function of f(x). Note that we can set out to find the 3rd derivative, 4th derivative, …, all the way to the nth derivative as desired. Any derivatives beyond the 1st derivative is called an higher order derivative.
Some of the practical applications of higher order derivatives includes finding acceleration and jerk functions. The second derivative in a particular is very useful in determining points of concavity of a function along with the intervals of concavity.