A Tabela Derivadas

TABELA DE DERIVADAS

FUNÇÃO f (x)	DERIVADA f’(x)
K	0
X	1
Xn	n.Xn-1
ex	ex
[pic 1]	[pic 2]
ln x	[pic 3]
sen x	cos x
cos x	- sen x
tg x	sec2x
arctg x	[pic 4]
arcsen x	[pic 5]
arccos x	[pic 6]
arccosec x	[pic 7]
arcsec x	[pic 8]
ax	ax.ln a
(1+2x)1/2	[pic 9]
ua	a.ua-1.u’

PROPRIEDADES DERIVADAS

[pic 10]                        [pic 11].

2.        [pic 12]                [pic 13].

3.        [pic 14]                        [pic 15].

4.        [pic 16]                        [pic 17].

5.        [pic 18]                        [pic 19].

6.        [pic 20]                [pic 21].

7.        [pic 22]                [pic 23].

TABELA DE PRIMITIVAS

FUNÇÃO f (x)	DERIVADA f’(x)
n≠ -1[pic 24]	[pic 25]
[pic 26]	ln x
ex	ex
[pic 27]	[pic 28]
cos x	sen x
sen x	- cos x
sec2 x	tg x
secx tgx	sec x
[pic 29]	sen-1 x
[pic 30]	tg-1 x
cosh x	senh x
[pic 31]	[pic 32]
c f(x)	c F(x)
f(x) + g(x)	F(x) + G(x)

TABELA SENO/COSSENO/TANGENTE

	0	30	45	60	90
SEN	0	[pic 33]	[pic 34]	[pic 35]	1
COS	1	[pic 36]	[pic 37]	[pic 38]	0
TG	0	[pic 39]	1	[pic 40]	∞
	0	TT/2	TT	3TT/2	2TT
SEN	0	1	0	-1	0
COS	1	0	-1	0	1

        

IDENTIDADES TRIGONOMÉTRICAS

sen2 + cos2 = 1	sen a – sen b = 2.sen(a-b/2). cos(a+b/2)
sen (a+b) = sen a. cos b + sen b. cos a	cosen a – cosen b = - 2.sen(a+b/2). sen(a-b/2)
sen (a-b) = sen a. cos b - sen b. cos a	1 + tg2 x = sec2 x
cos (a+b) = cos a. cos b – sen a. sen b	1 + cotg2 x = cossec2 x
cos (a-b) = cos a. cos b + sen a. sen b	sen 2x = 2 senx cosx