Delta derivative of quotient

Theorem

Let $\mathbb{T}$ be a time scale, $t \in \mathbb{T}^{\kappa}$, $f,g \colon \mathbb{T} \rightarrow \mathbb{R}$ delta differentiable, and $g(t)g(\sigma(t)) \neq 0$. Then $\dfrac{f}{g}$ is delta differentiable and $$\left( \dfrac{f}{g} \right)^{\Delta}(t) = \dfrac{g(t)f^{\Delta}(t)-f(t)g^{\Delta}(t)}{g(t)g(\sigma(t))},$$ where $\sigma$ denotes the forward jump.

References

• Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Theorem 1.20 (v)