# Derivative of x is 1

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 $y = x$ in the above equation, we get

Dividing both sides by $\Delta x$, we get

Taking limit of both sides as $\Delta x \to 0$, we have

Limit does not effect on constant values, so

This shows that the derivative of x is 1.

Example: Find the derivative of $y = f\left( x \right) = 7x$
We have the given function as

Differentiation with respect to variable $x$, we get

Now using the formula for constant function $\frac{d}{{dx}}\left( x \right) = 1$, we have