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FÓRMULAS BÁSICAS DE DERIVADAS E INTEGRAIS [Digite o nome da empresa] Função Derivada ( ) ,f u k k= ∈ℜ ´( ) 0f u = ( ) ,nf u u n= ∈ℜ 1(´ ) . nf u n u −= ( ) . ( )f u k f u= (´ ) . 'f u k f (u)= ( )f u u= '( ) 1f u = vuxf .)( = '( ) . ' '.f x u v u v= + v u xf =)( ' '. . '( ) ² u v u vf x v − = ( ) logaf u u= 1 '( ) ln f x u a = ( ) ,0 1uf u a a= < ≠ '( ) .lnuf u a a= ( ) lnf u u= 1 '( )f u u = ( )f u sen u= '( ) cosf u u= ( ) cosf u u= '( )f u sen u= − ( )f u tg u= 2'( ) secf u u= ( )f u sec u= '( )f u sec u .tg u= ( )f u cossec u= '( )f u -cotg u.cossec u= ( )f u cotg u= '( ) 2f u cossec u= − ( ) uf u e= '( ) uf u e= ( )f u arc cosu= 2 1 '( ) 1 f u u = − − ( )f u arc senu= 2 1 '( ) 1 f u u = − ( )f u arc tg u= 2 1 '( ) 1 f u u = + Integral Primitiva du =∫ u c+ k du =∫ .k u c+ nu du =∫ 1 1 n u c n + + + du u =∫ ln u c+ senu du =∫ cosu c− + cosu du =∫ senu c+ 2sec u du∫ tg u c+ 2cosec u du =∫ cotg u + c− secu.tg u du =∫ secu+c ue du =∫ ue c+ ua du =∫ ( 0, 1) ln u a c a a a + > ≠ 2 1 1 u = − ∫ arc sen u + c 2 1 1 x = + ∫ arc cos u + c 2 1 1 x = +∫ arc tg u c+ sen ax dx =∫ 1 cos ax c a − + cos ax dx =∫ 1 sen ax c a +
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