For a differentiable function , the new function created by associating each element of the domain with its derivative is called the derivative of the function . It is denoted by the symbols:
That is,
The process of finding the derivative of a function with respect to is called differentiation, and the method for doing so is called the differentiation method.
Derivative of the function ( is a natural number) and constant functions
If (where is a natural number), then:
When ,
When ,
If (where is a constant), then
Differentiation Rules
Differentiation rules for scalar multiples, sums, and differences of functions
When two functions and are differentiable:
If (where is a constant), then
If , then
If , then
Differentiation rules for products of functions
When three functions , , and are differentiable: