(related to Corollary: Derivative of a Constant Function)
Given a constant function \(f:\mathbb R\to\mathbb R\), \(f(x)=c\), \(c\in\mathbb R\), and by definition is of the derivative we have
\[f'(x)=\lim_{\substack{\xi\to x\\\xi\neq x}}\frac {f(\xi)-f(x)}{\xi-x}=\frac{c-c}{\xi-x}=0.\]
