how i can understand differentiation and its basics????

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)

x-> x0