# Constant derivative rule/Proof

877pages on
this wiki

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

## PrerequisitesEdit

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

## ProofEdit

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