Question

How to use signum function

Answer 1

The signum function is differentiable with derivative 0 everywhere except at 0. It is not differentiable at 0 in the ordinary sense, but under the generalised notion of differentiation in distribution theory, the derivative of the signum function is two times the Dirac delta function, which can be demonstrated using the identity

\displaystyle \operatorname {sgn}(x)=2H(x)-1\,}

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