The q-analog of the derivative, defined by (d/(d x))_q f(x) = (f(x) - f(q x))/(x - q x). For example, (d/(d x))_q sin x | = | (sin x - sin(q x))/(x - q x) (d/(d x))_q ln x | = | (ln x - ln(q x))/(x - q x) = (ln(1/q))/((1 - q) x) (d/(d x))_q x^2 | = | (x^2 - q^2 x^2)/(x - q x) = (1 + q) x (d/(d x))_q x^3 | = | (x^3 - q^3 x^3)/(x - q x) = (1 + q + q^2) x^2. In the limit q->1, the q-derivative reduces to the usual derivative.
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