q-derivatives of multivariable q-hypergeometric function with respect to their parameters

Abstract: 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.