Delta derivative at right-scattered
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Theorem
Let $\mathbb{T}$ be a time scale. Let $f \colon \mathbb{T} \rightarrow \mathbb{R}$ be continuous and right-scattered at $t \in \mathbb{T}$. Then $$f^{\Delta}(t)=\dfrac{f(\sigma(t))-f(t)}{\mu(t)},$$ where $f^{\Delta}$ denotes the delta derivative, $\sigma$ denotes the forward jump, and $\mu$ denotes the forward graininess.
Proof
References
- Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Theorem 1.16
