The physical concept describes the differentiation as the process that helps us to understand how things change over time. Many real word applications are represented by functions that simulate the behavior of these applications. The differentiation of the equations of these functions helps us to find out the rates of change of the corresponding real world applications.
The mathematical modelling using algebraic functions is used in economics (logistic functions used for describing the growth or decline of an industry), engineering, medicine, growth processes, business, etc.
The geometrical approach of derivative describes it as being the slope of tangent line to a curve, at a given point.
We'll consider the function y = f(x) and we want to determine the derivative of the function, at the point x = x0.
This derivative represents the slope of the tangent line, at the graph of this function f(x), at the point x = x0
m = lim [f(x) - f(x0)]/(x - x0)