Difference between revisions of "Delta derivative of product (1)"

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(Created page with "==Theorem== Let $\mathbb{T}$ be a time scale and $f,g \colon \mathbb{T} \rightarrow \mathbb{R}$ delta differentiable. Then the product function $fg$ i...")
 
 
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==References==
 
==References==
* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta derivative of constant multiple|next=Delta derivative of product (2)}: Theorem 1.20 (iii)
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* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta derivative of constant multiple|next=Delta derivative of product (2)}}: Theorem 1.20 (iii)
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[[Category:Theorem]]
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[[Category:Unproven]]

Latest revision as of 05:45, 10 June 2016

Theorem

Let $\mathbb{T}$ be a time scale and $f,g \colon \mathbb{T} \rightarrow \mathbb{R}$ delta differentiable. Then the product function $fg$ is delta differentiable with $$(fg)^{\Delta}(t)=f^{\Delta}(t)g(t)+f(\sigma(t))g^{\Delta}(t),$$ where $\sigma$ denotes the forward jump.

Proof

References