# Delta derivative of sum

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