Tabela de Derivadas e Teoremas Básicos

Tabela de Derivadas e Teoremas Básicos :

f ´(x) = lim _ f (x) - f (xo) _ x→ x. x - xo f ´(x) = lim _ f (xo+ h) - f (xo) _ , h = x - xo h→0 h

d/dx
[ un ] = n u n-1 du/dx d/dx
[ sen u ] = cos u du/dx d/dx
[ cos u ] = - sen u du/dx d/dx
[ tg u ] = sec 2 u du/dx d/dx
[ sec u ] = sec u . tg u du/dx d/dx
[ cossec u ] = - cossec u . cotg u du/dx d/dx
[ cotg u ] = - cossec2 u du/dx d/dx
[ eu ] = eu du/dx d/dx
[ au ] = au ln a du/dx d/dx
[ log a u ] = _ 1 _ du/dx u ln a d/dx
[ ln u ] = _ 1 _ du/dx u d/dx
[ arc sen u ] = _ 1‗‗‗‗‗_ du/dx √1 – u2 d/dx
[ arc cos u ] = _ - 1‗‗‗‗‗_ du/dx √1 –u2 _ d/dx
[ arc tg u ] = _ 1 _ du/dx 1 – u2 d/dx
[ arc co tg u ] = _ - 1 _ du/dx 1 – u2 d/dx
[ arc sec u ] = _ 1‗‗‗‗‗_ du/dx | u | √ u2 - 1 d/dx
[ arc cossec u ] = _ - 1‗‗‗‗‗_ du/dx | u | √ u2 - 1

d/dx
[ f (x) . g (x) ] = f ´(x) . g (x) + f (x) . g ´(x) d/dx
[ f (x) / g (x) ] =_ g (x) . f ´(x) - f (x) . g ´(x) _ [ g (x) ] 2

L´Hopital : usa-se no lim indeterminado 0/0 ou ∞/∞ lim _ f (x) _ = lim _ f ´ (x) _ x→ a g (x) LH x→ a g ´(x) ∞.0 → mantém o 1º e divide pelo inverso do 2º ∞ - ∞ → m.m.c. 00 , ∞0 e 1∞ → aplica ln dos 2 lados