Difference between revisions of "Delta derivative of reciprocal"
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==References== | ==References== | ||
* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta derivative of product (2)|next=Delta derivative of quotient}}: Theorem 1.20 (iv) | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta derivative of product (2)|next=Delta derivative of quotient}}: Theorem 1.20 (iv) | ||
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Latest revision as of 15:19, 21 January 2023
Theorem
Let $\mathbb{T}$ be a time scale, $t \in \mathbb{T}^{\kappa}$, $f \colon \mathbb{T} \rightarrow \mathbb{R}$ delta differentiable, and $f(t)f(\sigma(t)) \neq 0$. Then $\dfrac{1}{f}$ is delta differentiable and $$\left( \dfrac{1}{f} \right)^{\Delta}(t) = -\dfrac{f^{\Delta}(t)}{f(t)f(\sigma(t))},$$ where $\sigma$ denotes the forward jump.
References
- Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Theorem 1.20 (iv)
