  First derivatives with respect to the parameters of the Whittaker function
$\mathrm{W}_{\kappa ,\mu }\left( x\right) $ are calculated. Using the confluent
hypergeometric function, these derivarives can be expressed as infinite sums of
quotients of the digamma and gamma functions. Also, it is possible to obtain
these parameter derivatives in terms of infinite integrals with integrands
containing elementary functions (products of algebraic, exponential and
logarithmic functions) from the integral representation of $\mathrm{W}_{\kappa
,\mu }\left( x\right) $. These infinite sums and integrals can be expressed in
closed-form for particular values of the parameters. Finally, an integral
representation of the integral Whittaker function $\mathrm{wi}_{\kappa ,\mu
}\left( x\right) $ and its derivative with respect to $\kappa $, as well as
some reduction formulas for the integral Whittaker functions
$\mathrm{Wi}_{\kappa ,\mu }\left( x\right) $ and $\mathrm{wi}_{\kappa ,\mu
}\left( x\right) $ are calculated.
