Higher-Order Derivatives

It can be seen that the derivative of a function is also a function.

Considering f'x as a function of x, we can take the derivative of  f'x which will yield another function, say f''x. This is called the second derivative of f(x). The third derivative of f(x) is the derivative of the second derivative f''x. We can take derivatives of higher orders by repeating the process. The second, third, fourth, (etc.) derivatives are symbolically written as:

Example