Q-derivative

The $q$-derivative is $$\left(\dfrac{d}{dx} \right)_q f(x) =D_q\{f\}(x)=\left\{ \begin{array}{ll} \dfrac{f(qx)-f(x)}{qx-x} &; x \neq 0 \\ f'(0) &; x=0. \end{array} \right.$$

Properties

Relationship between q-derivative and derivative
q-derivative power rule