differentiable function

In mathematics, a differentiable function is one for which the derivative can be found at a given point. The derivative represents the instantaneous rate of change of a quantity or the slope of a curve at that specific point.1

For a function to be differentiable at a point, it must first be continuous at that point. However, being continuous does not guarantee differentiability.1

The concept of differentiability is crucial in calculus, where it is used to understand how quantities change and to find maximum and minimum values of functions. In the realm of complex numbers, differentiability implies a much stronger property, known as analyticity, meaning that if the first derivative exists, all higher derivatives also exist and the function can be represented by a power series.12