The derivative of x is 1 (one). Now by definition or first principle we shall show that derivative of x is equal to 1 .
Let us suppose that
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 limit of both sides as , we have
Limit does not effect on constant values, so
This shows that the derivative of x is 1.
Example: Find the derivative of
We have the given function as
Differentiation with respect to variable , we get
Now using the formula for constant function , we have