Difference between revisions of "Delta derivative of constant multiple"

From timescalewiki
Jump to: navigation, search
Line 6: Line 6:
  
 
==References==
 
==References==
* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta derivative of sum|next=Delta derivative of product (1)}}: Theorem 1.20 (iii)
+
* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta derivative of sum|next=Delta derivative of product (1)}}: Theorem 1.20 (ii)

Revision as of 05:36, 10 June 2016

Theorem

Let $\mathbb{T}$ be a time scale, $\alpha \in \mathbb{R}$, and $f \colon \mathbb{T} \rightarrow \mathbb{R}$ delta differentiable. Then the function $\alpha f$ is delta differentiable with $$(\alpha f)^{\Delta}(t)=\alpha f^{\Delta}(t).$$

Proof

References