Derivative of Constant

Theorem
Let $$f_c \left({x}\right)$$ be the constant function on $$\R$$, where $$c \in \R$$.

Then $$f_c^{\prime} \left({x}\right) = 0$$.

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

Thus:

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