Determining If a Heaviside Function Has a Derivative at 0

Determine if the Heaviside function \(u_{0}( t) =\left\{ \begin{array}{l@{\quad}ll} 0 & \hbox{if} & t < 0 \\ 1 & \hbox{if} & t ≥ 0 \end{array} \right.\) has a derivative at \(0.\)

Solution Since \(u_{0}( t)\) is discontinuous at 0, it has no derivative at 0.