Constant derivative rule/Proof

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$\frac{d}{dx}a=0$, for some constant a.

Prerequisites

The limit definition of the derivative, $f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}$

Proof

Let f(x) = a for some constant a. From the limit definition of the derivative:

$f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}$
$f'(x)=\lim_{h \to 0}\frac{a-a}{h}$
$f'(x)=0$

QED