Now that we understand the derivative of f(x) as a function, we can keep differentiating to define the higher derivatives of function f(x). For example, the second derivative of f(x) at point x=a is defined to be the derivative of the function f'(x) at x=a, at least if f'(x) is differentiable at x=a. Furthermore, in the same way we defined the function f'(x), we can then collect the (second) derivatives f''(a) into a function f''(x), which can then be differentiated at any point to get third derivatives, and so on.