Tabela das principais derivadas -

Nesta página apresenta-se a Tabela das principais derivadas, ou seja, as derivadas que mais aparecem na resolução das listas de exercícios.

FUNÇÃO	DERIVADA
$y(x)=C$	$y'(x)=0$
$y(x)=C\cdot u(x)$	$y'(x)=C\cdot u'(x)$
$y(x)=x^{n}$	$y'(x)=n\cdot x^{n-1}$
$y(x)=e^{u(x)}$	$y'(x)=e^{u(x)} \cdot u'(x)$
$y(x)=a^{u(x)}$	$y'(x)=a^{u(x)} \cdot \ln a \cdot u'(x)$
$y(x)=\ln u(x)$	$\displaystyle y'(x)=\frac{u'(x)}{u(x)}$
$y(x)=\log_{a}u(x)$	$\displaystyle y'(x)=\frac{u'(x)}{u(x)\cdot \ln a}$
$y(x)= sen\, u(x)$	$y'(x)= cos\, u(x)\cdot u'(x)$
$y(x)= cos\, u(x)$	$y'(x)= -sen\, u(x)\cdot u'(x)$
$y(x)= tg\, u(x)$	$y'(x)= sec^{2}\, u(x) \cdot u'(x)$
$y(x)= cotg\, u(x)$	$y'(x)= -cossec^{2}\, u(x) \cdot u'(x)$
$y(x)= sec\, u(x)$	$y'(x)= sec\, u(x) \cdot tg\,u(x) \cdot u'(x)$
$y(x)= cossec\, u(x)$	$y'(x)= -cossec\, u(x) \cdot cotg\, u(x)\cdot u'(x)$
$y(x)= senh\, u(x)$	$y'(x)= cosh\, u(x)\cdot u'(x)$
$y(x)= cosh\, u(x)$	$y'(x)= senh\, u(x)\cdot u'(x)$
$y(x)= tgh\, u(x)$	$y'(x)= sech^{2}\, u(x) \cdot u'(x)$
$y(x)= cotgh\, u(x)$	$y'(x)= -cossech^{2}\, u(x) \cdot u'(x)$
$y(x)= sech\, u(x)$	$y'(x)= -sech\, u(x) \cdot tgh\,u(x) \cdot u'(x)$
$y(x)= cossech\, u(x)$	$y'(x)= -cossech\, u(x) \cdot cotgh\, u(x)\cdot u'(x)$

110 Questões Resolvidas de Cálculo Diferencial