u-v-u-v-tow-fonctions-

Question Number 135536 by islamo last updated on 13/Mar/21

{(u^{v})}^{'} = ?

u, v t o w f o n c t i o n s

Answered by Olaf last updated on 13/Mar/21

u^{v} = e^{\ln (u^{v})} = e^{v \ln u}

{(u^{v})}^{'} = {(v \ln u)}^{'} e^{v \ln u} = (v^{'} \ln u + \frac{{v u}^{'}}{u}) u^{v}

{(u^{v})}^{'} = v^{'} u^{v} \ln u + u^{'} {v u}^{v - 1}

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