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*<math> \left| \frac {\tan(x+iy) }{x+iy} \right| </math>
;First-order derivative
*<math> \frac {1- (\tan(z))^2}{z} - \frac {\tan(z)}{z^2} </math>
;Real part of derivative
*<math> -\operatorname{Re} \left( -\frac {1- (\tan(x+iy))^2}{x+iy} +\frac{\tan(x+iy)}{(x+iy)^2} \right)
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