Delta derivative of squaring function

Theorem

Let $\mathbb{T}$ be a time scale. The following formula holds for $f \colon \mathbb{T} \rightarrow \mathbb{R}$ defined by $f(t)=t^2$: $$f^{\Delta}(t)=t+\sigma(t),$$ where $f^{\Delta}$ denotes the delta derivative and $\sigma$ denotes the forward jump.