  We consider the q-derivatives of the Srivastava and Daoust basic
multivariable hypergeometric function with respect to the parameters. This
function embodies a entire number of various q-hypergeometric series of one and
several variables.
  Explicit equations are given for general case of summation indexes with
positive real coefficients. As an example derivatives of q-analog of
non-confluent Horn type hypergeometric function $H_3$ is presented.
