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26 {Ëîãàðèôìè÷åñêàÿ ïðîèçâîäíàÿ} y=[u(x)]v(x),u(x)>0; lny=v(x)lnu(x); y'/y=v’(x)lnu(x)+v(x)?u’(x)/u(x); y’=uv?(v’lnu+v?u’/u); (lny)’=y’/y-ëîãàðèôìè÷åñêàÿ ïðîèçâîäíàÿ ô-öèè {Ïðîèçâîäíûå îñíîâíûõ ýëåìåíòàðíûõ ô-öèé} 1) y=Const Dy=c-c=0?limDx®0Dy/Dx?(C)’=0 ; 2) y=sinx Dy’=cosx 3)(cosx)’=-sinx 4) (ax)’=axlna 5)(arcsinx)’=1/?1-x? 6)(arccosx)’=-1/?(1-x?) 7) (arctgx)’=1/(1+x?) 8) (arcctgx)’=-1/(1+x?) 9) (lnx)’=1/x ; 10) (xa)’=a?xa-1