Derivative of alternative delta sine

Theorem

Let $\mathbb{T}$ be a time scale. The following formula holds: $$\mathrm{s}_{pq}^{\Delta}(t,s;\mathbb{T})=q(t)\mathrm{c}_{pq}(t,s;\mathbb{T})+p(t)\mathrm{s}_{pq}(t,s;\mathbb{T}),$$ where $\mathrm{s}_{pq}$ denotes the alternative delta sine and $\mathrm{c}_{pq}$ denotes the alternative delta cosine.