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

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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$D_q(z^n)=[n]_q z^{n-1},$$ where $D_q$...") |
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− | + | ==Theorem== | |

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

− | + | ||

− | + | ==Proof== | |

− | + | ||

− | + | ==References== | |

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+ | [[Category:Theorem]] | ||

+ | [[Category:Unproven]] |

## Revision as of 22:31, 16 June 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 $q$-factorial.