  In this paper, we investigate applications of the ordinary derivative
operator, instead of the $q$-derivative operator, to the theory of $q$-series.
As main results, many new summation and transformation formulas are established
which are closely related to some well-known formulas such as the $q$-binomial
theorem, Ramanujan's ${}_1\psi_1$ formula, the quintuple product identity,
Gasper's $q$-Clausen product formula, and Rogers' ${}_6\phi_5$ formula, etc.
Among these results is a finite form of the Rogers-Ramanujan identity and a
short way to Eisenstein's theorem on Lambert series.
