The wikipedia article on [itex]\sgn (x)[/itex] (http://en.wikipedia.org/wiki/Sign_function) states that,(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\frac{d}{dx}\vert x\vert = \sgn(x)

[/tex]

and [itex]\frac{d}{dx}\sgn(x) = 2\delta(x)[/itex]. I'm wondering why the following is not true:

[tex]

\begin{align*}

\vert x\vert &= x\sgn(x)\\

\Longrightarrow \frac{d}{dx}\vert x \vert &= \sgn(x) + 2x\delta(x)

\end{align*}

[/tex]

by the product rule for derivatives. Is it because this derivative is indeterminate at [itex]x=0[/itex], and [itex]2x\delta(x) \equiv 0 [/itex] for all [itex]x \neq 0[/itex]?

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# Derivatives of |x|

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