Derivative of a Function

The derivative of a given function y = f(x) is defined as the limit of the ratio of the increment ∆y of the function to the corresponding increment ∆x of the independent variable, when the latter tends to zero.

Derivative of f(x) at a is denoted by f'(x). f'(a) quantifies the change in f(x) at a with respect to x.

Suppose f is a real valued function and a is a point in its domain of definition. The derivative of f at a is defined by

  

This definition of derivative is also called the first principle of derivative.

The operation of finding the derivative is called differentiation.

Derivative of Polynomial Functions

Derivative of Trigonometric Functions

Derivative of Inverse T-Functions

Derivative of Exponential & Log Functions