The derivative of a constant function is zero. Now we shall prove this constant function with the help of the definition of derivative or differentiation.
Let us suppose that where is any real constant.
First we take the increment or small change in the function:
Putting the value of function in the above equation, we get
Dividing both sides by , we get
Taking the limit of both sides as , we have
This shows that the derivative of a function is zero.
Example: Find the derivative of
We have the given function as
Differentiating with respect to variable , we get
Now using the formula for a constant function , we have