Derivative of Identity Function

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

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

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

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

Thus:

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