Derivative of Identity Function

Theorem
Let $$I_\R: \R \to \R$$ be the identity function.

Then $$\forall x \in \R: I_\R^{\prime} \left({x}\right) = 1$$.

Note that this can be more compactly written $$D_x \left({x}\right) = 1$$.

Proof
The identity function is defined as $$\forall x \in \R: I_\R \left({x}\right) = x$$.

Thus:

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