# The \(n\)th derivative \(f^{(n)} of the function \(f: \mathbb{R}\rightarrow \mathbb{R}\) defined by \(f(x)=|x|\) for all \(x\in\mathbb{R}\) is

The \(n\)th derivative \(f^{(n)} of the function \(f: \mathbb{R}\rightarrow \mathbb{R}\) defined by \(f(x)=|x|\) for all \(x\in\mathbb{R}\) is

\(f'(x)=\left\{\begin{array}{rcl}-x&\mbox{if}&x> 0\\x&\mbox{if}&x<0\end{array}\right}\).

\(f'(x)=\left\{\begin{array}{rcl}-1&\mbox{if}&x> 0\\1&\mbox{if}&x<0\end{array}\right}\).

\(f'(x)=\left\{\begin{array}{rcl}x&\mbox{if}&x> 0\\-1&\mbox{if}&x<0\end{array}\right}\).

—>> \(f'(x)=\left\{\begin{array}{rcl}1&\mbox{if}&x> 0\\-1&\mbox{if}&x<0\end{array}\right}\).