Derivadas e integrais
Por: Marina Souza • 29/3/2016 • Exam • 639 Palavras (3 Páginas) • 338 Visualizações
UNIVERSIDADE FEDERAL DO ABC
Tabela de Derivadas, Integrais e Identidades Trigonom ́etricas
Derivadas
Regras de Deriva ̧c ̃ao
• (cf(x)) = cf (x)
• Derivada da Soma
(f(x) + g(x)) = f (x) + g (x)
• Derivada do Produto
(f(x)g(x)) = f (x)g(x) + f(x)g (x)
• Derivada (
f(x)
do Quociente
g(x)
Fun ̧c ̃oes Trigonom ́etricas Inversas
• d dx
arcsen x = √
1−x2
1
• dx d
arccosx = √
1−x2 −1
• d dx
arctg x = 1+x2
1
)
=
f (x)g(x) g(x)2
− f(x)g (x)
• d dx
arcsecx = |x|
√
x2−1 1
• d dx
• Regra da Cadeia
(f(g(x)) = (f (g(x))g (x)
Fun ̧c ̃oes Simples
• d dx
arccotg x = 1+x2
−1
• d dx
arccossec x = |x|
√
−1
x2−1
Fun ̧c ̃oes Hiperb ́olicas c = 0
• dx d
x = 1
• d dx
senh x = coshx = ex+e−x
2
• dx d
cx = c
• dx d
coshx = senh x = ex−e−x
2
• dx d
xc = cxc−1
• d dx
• d dx
(
1
2
x
• d dx
tgh x = sech
x
)
= dx
d
(
x−1
)
= −x−2 = − x2 1
• d dx
(
1 xc
)
= dx
d
(x−c)=− xc+1
c
sech x = − tgh x sech x
• dx d
√
x = dx
d
x
1 2
= 1 2
x− 1 2
= 2
√ 1
x
,
• d dx
cotgh x = − cossech
2
x
Fun ̧c ̃oes Exponenciais e Logarıtmicas
Fun ̧c ̃oes Hiperb ́olicas Inversas
• dx d
ex = ex
• d dx
ln(x) = x 1
• d dx
csch x = − coth x cossech x
• dx d
ax = ax ln(a)
• d dx
arcsenh x = √
x2+1
1
Fun ̧c ̃oes Trigonom ́etricas
• d dx
• d dx
arccosh x = √
x2−1
1
senx = cos x
• dx d
cosx = −sen x,
• d dx
arctgh x = 1−x2
1
• d dx
tg x = sec2 x
• d dx
• d dx
arcsech x = x
√
−1
1−x2 secx = tg xsecx
• d dx
cotg x = −cossec 2x
• d dx
arccoth x = 1−x2
1
• d dx
cossec x = −cossec x cotg x
• d dx
arccossech x = |x|
√
−1
1+x2
1
Integrais
Regras de Integra ̧c ̃ao
•
∫
cf(x)dx = c
∫
f(x)dx
•
∫
u
√
1 du
+ u2
= −arccosech |u| + c
•
∫
[f(x) + g(x)]dx =
∫
f(x)dx +
∫
g(x)dx
•
∫
√
a2 1
− x2
x a
•
+ c
•
dx = arcsen ∫
f (x)g(x)dx = f(x)g(x) −
∫
f(x)g (x)dx
Fun ̧c ̃oes Racionais
•
∫
√
a2 −1
− x2
a x
+ c
Fun ̧c ̃oes Trigonom ́etricas
•
dx = arccos
∫
xn dx = xn+1 n+1
+ c para n = −1
•
∫
x 1
dx = ln|x|+ c
∫
cosx dx = senx+ c
•
•
∫
du 1 + u2
∫
senx dx = −cosx+ c
= arctgu + c
•
∫
tgx dx = ln|secx|+ c
•
∫
a2 + 1
x2
dx =
a 1
arctg(x/a) + c
•
∫
cscx dx = ln|cscx − cotx| + c
•
•
∫
du
{
arctgh u + c, se |u| < 1
∫
secx dx = ln|secx + tgx|+ c
1 2
1 − \
\1+u 1−u u2
= \ \
+ c
arccotgh u + c, se |u| > 1
=
•
∫
cotx dx = ln|senx|+ c
•
Fun ̧c ̃oes Logarıtmicas
•
ln
∫
secxtgx dx = secx + c
•
∫
cscxcotx dx = −cscx + c ∫
...