Q-derivative of q-Cosine

Theorem

The following formula holds: $$D_q \mathrm{Cos}_q(az) = -a \mathrm{Sin}_q(az),$$ where $D_q$ denotes the q-derivative, $\mathrm{Cos}$ denotes the $q$-Cosine function, and $\mathrm{Sin}$ denotes the $q$-Sine function.

References

• 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous): (6.171)