Delta derivative of sum
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Theorem
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 $$(f+g)^{\Delta}(t)=f^{\Delta}(t)+g^{\Delta}(t).$$
Proof
References
- Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Theorem 1.20 (ii)
