Calculus - Higher Order Derivatives

In calculus, higher order derivatives are derivatives of a function f taken n times. They are denoted as f^(n)(x). When n is 2, we often refer to it as the second derivative, when n is 3, the third derivative, and so on. To find higher order derivatives, we apply the standard derivative rules (such as the power rule, product rule, and chain rule) repeatedly until we reach the nth derivative.

These higher order derivatives have important applications in physics and engineering, particularly in the study of motion where the second derivative represents acceleration, and higher derivatives can represent jerk and other rates of change of acceleration. In mathematics, the Taylor series uses higher order derivatives to approximate functions near a specific point.