Derivative of Identity Function

Theorem
Let $X$ be either set of either the real numbers $\R$ or the complex numbers $\C$.

Let $I_X: X \to X$ be the identity function.

Then:
 * $I_X' \left({x}\right) = 1$

where $I_X' \left({x}\right)$ denotes the derivative of $I_X$ $x$.

This can be presented for each of $\R$ and $\C$:

Also presented as
Note that this can be written:
 * $D_x \left({x}\right) = 1$

Using Leibniz's notation for derivatives it can also be stated as:
 * $\dfrac {\mathrm d x} {\mathrm d x} = 1$