# How do I use the limit definition of derivative to find f'(x) for f(x)=c ?

Sep 20, 2014

$f \left(x\right) = c$ is a constant function, so its value stays the same regardless of the x-value. In particular, $f \left(x + h\right) = c$.

By the definition of the derivative,

$f ' \left(x\right) = {\lim}_{h \to 0} \frac{f \left(x + h\right) - f \left(x\right)}{h}$

$= {\lim}_{h \to 0} \frac{c - c}{h}$

$= {\lim}_{h \to 0} 0$

$= 0$