# Delta derivative of constant multiple

Let $\mathbb{T}$ be a time scale, $\alpha \in \mathbb{R}$, and $f \colon \mathbb{T} \rightarrow \mathbb{R}$ delta differentiable. Then the function $\alpha f$ is delta differentiable with $$(\alpha f)^{\Delta}(t)=\alpha f^{\Delta}(t).$$