deletions | additions       diff --git a/DeclareMathOperator_argmin_argmin_newcommand_reals__.tex b/DeclareMathOperator_argmin_argmin_newcommand_reals__.tex  index 2c01640..d1e89b0 100644  --- a/DeclareMathOperator_argmin_argmin_newcommand_reals__.tex  +++ b/DeclareMathOperator_argmin_argmin_newcommand_reals__.tex 
...
where $\mu$ is a positive smoothing parameter. With this approximation,  applying the definition of the complex derivatives yields  \begin{eqnarray}  D|x| &=& \partial{d|x|}{da} \frac{d|x|}{da}  + j\partial{d|x|}{db} j\frac{d|x|}{db}  \nonumber\\ &\approx& \partial{d\sqrt{a^2+b^2 \frac{d\sqrt{a^2+b^2  + \mu}}{da} + j\partial{d\sqrt{a^2+b^2 j\frac{d\sqrt{a^2+b^2  + \mu}}{db} \nonumber \end{eqnarray}