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[[File:Sinhc 2D plot.png|thumb|Sinhc 2D plot]]
[[File:Sinhc'(z) 2D plot.png|thumb|Sinhc'(z) 2D plot]]
[[File:Sinhc integral 2D plot.png|thumb|Sinhc integral 2D plot]]The first-order derivative is given by
;Imaginary part in complex plane
:<math> \operatorname{Im} \left( \frac {\sinh(x+iy) }{x+iy} \right) </math>
;Real part in complex plane
:<math> \operatorname{Re} \left( \frac {\sinh(x+iy) }{x+iy} \right) </math>
;absolute magnitude
:<math> \left| \frac {\sinh(x+iy) }{x+iy} \right| </math>
;First-order derivative
:<math> \frac {\cosh(z)}{z} - \frac {\sinh(z)}{z^2} </math>
;Real part of derivative
:<math> -\operatorname{Re} \left( -\frac {1- (\sinh(x+iy))^2}{x+iy} +\frac{\sinh(x+iy)}{(x+iy)^2} \right) </math>
;Imaginary part of derivative
:<math>-\operatorname{Im} \left( -\frac {1-(\sinh(x+iy))^2}{x+iy} + \frac {\sinh(x+iy)}{(x+iy)^2} \right) </math>
;absolute value of derivative
:<math> \left| -\frac{1-(\sinh(x+iy))^2}{x+iy}+\frac {\sinh(x+iy)}{(x+iy)^2} \right| </math>
==In terms of other special functions==
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