3.31 Higher-order derivatives

Starting from $f(x)$, we can form the first derivative $f^{\prime}(x).$ We suppose that we can differentiate this function again to form the second derivative $f^{\prime\prime}(x)$, and so on. We denote the $n^{th}$ derivative by $f^{(n)}(x)$, or in Leibniz’s notation as

The number of times that $f$ is differentiated is called the order of the derivative.