# Difference between revisions of "Delta derivative of constant multiple"

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==Theorem== | ==Theorem== | ||

− | Let $\mathbb{T}$ be a [[time scale]] and $f | + | Let $\mathbb{T}$ be a [[time scale]], $\alpha \in \mathbb{R}$, and $f \colon \mathbb{T} \rightarrow \mathbb{R}$ [[delta derivative|delta differentiable]]. Then the function $\alpha f$ is delta differentiable with |

− | $$( | + | $$(\alpha f)^{\Delta}(t)=\alpha f^{\Delta}(t).$$ |

− | |||

==Proof== | ==Proof== |

## 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

- Martin Bohner and Allan Peterson:
*Dynamic Equations on Time Scales*(2001)... (previous)... (next): Theorem 1.20 (iii)