Derivative at a Point

 

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.