tabela derivadas e integrais

Prévia do material em texto

Constante 
	f (x) = a 
	f '(x) = 0 
	Afim
	f (x) = ax + b
	f '(x) = a
	Identidade
	f(x) = x
	f '(x) = 1
	Potência
	f (x) = xn 
	f '(x) = n . xn – 1
	Logarítmica
	f (x) = loga(x) 
(x ∈ R*+ e 0 < a ≠ 1)
	
	Logarítmica
(Base Natural)
	f (x) = ln (x)
	
	Exponencial
(Base qualquer)
	f (x) = ax 
(a > 0) 
	f ' (x) = ax ∙ ln (a)
	Exponencial
(base Natural)
	f (x) = ex
	f' (x) = ex
	Seno
	f (x) = sen (x)
	f ' (x) = cos (x)
	Cosseno
	f (x) = cos (x)
	f ' (x) = -sen (x)
	Tangente
	f (x) = tg (x)
	f ' (x) = sec ² (x)
	Cotangente
	f (x) = cotg (x)
	f '(x) = -cossec ² (x)
	Secante
	f (x) = sec (x)
	f ' (x) = tg (x) ∙ sec (x)
	Cossecante
	f (x) = cossec (x)
	f ' (x) = -cotg (x) ∙ cossec (x)
	Arco-seno
	f (x) = arcsen (x)
	
	Arco-cosseno
	f (x) = arccos (x)
	
	Arco-tangente
	f (x) = arctg (x)
	
	Arco-cotangente
	f (x) = arccotg (x)
	
	Arco-secante
	f (x) = arcsecc (x)
	
	Arco-cossecante
	f (x) = arccossec (x)