Derivatives and Anti-derivativesThe derivative of a function is one of the basic concepts of mathematics. Together with the integral, derivative occupies a central place in calculus. The process of finding the derivative is called differentiation. The inverse operation for differentiation is called integration.
The derivative of a function at some point characterizes the rate of change of the function at this point. We can estimate the rate of change by calculating the ratio of change of the function Δy to the change of the independent variable Δx. In the definition of derivative, this ratio is considered in the limit as Δx → 0. Let us turn to a more rigorous formulation.
The chart below shows to differentiate and integrate the most common functions.
There are, Integration reverses differentiation, returning the function to its original state, up to a constant C.