# Difference between revisions of "Q-derivative power rule"

From specialfunctionswiki

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The following formula holds: | The following formula holds: | ||

$$D_q(z^n)=[n]_q z^{n-1},$$ | $$D_q(z^n)=[n]_q z^{n-1},$$ | ||

− | where $D_q$ denotes the [[q-derivative|$q$-derivative]] and $[n]_q$ denotes the [[q- | + | where $D_q$ denotes the [[q-derivative|$q$-derivative]] and $[n]_q$ denotes the [[q-number|$q$-number]]. |

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

## Revision as of 18:28, 20 September 2016

## Theorem

The following formula holds: $$D_q(z^n)=[n]_q z^{n-1},$$ where $D_q$ denotes the $q$-derivative and $[n]_q$ denotes the $q$-number.