Derivability or Differentiability at a Point
Let f be a function and a be any point in its domain. Let h>0 be a small number.f(x) is said to be differentiable if 
exists and is denoted by f|(a), then f|(a) is called the derivative or differential coefficient of f(x) at x = a. That is
Left Hand Derivative
as x approaches a through values less than 'a' is called Left hand derivative at x=a denoted by Lf '(a).
Right Hand Derivative
as x approaches a through values greater than 'a' is called Right hand derivative at x = a, denoted by Rf '(a).
Differentiation from First Principles
Let y = f (x).The derivative of f at x is denoted by f '(x).
Finding the derivative of a function using the above definition is called differentiation from first principles.
