Differentiation is considered an easy topic in calculus. Far more easier than integration, but Some functions are just made to be painful. Today i will be discussing with you guys the derivative of these functions . There are mainly 3 of them and . Let's Begin !
There are two ways to calculate the derivative of . If you know any other method , please share it in the comments section below.
The Result makes a lot of sense .... if , the Derivative is and if , Derivative is
This is indeed what the graph of tells us!
Now Let's take a general Case of , Where
When floor function or Greatest integer function is applied on a function , the range changes to integral values. We can say that the derivative of the function is when the function is continuous. The derivative does not exists at integer values of x, because the graph is discontinuous .
For a General , the derivative will always be .
When Fractional part function is applied on a function , the Range changes to .
can be written as . Using this property we will find the derivative of . The derivative does not exists at integer values of , because the graph is discontinuous .
For a General
I Hope you enjoyed this :)