DERIVADAS FORMULÁRIO

Prévia do material em texto

DERIVADAS 
01 y = k (constante) y’ = 0 LEMBRETES: 
 
02 
 
y = x 
 
y’ = 1 
 
sen2 a + cos 2 a = 1 
 
03 
 
y = u + v - z 
 
y’ = u´+ v´- z´ 
 
 
04 
 
y = k.u 
 
y’ = k.u´ 
 
sec 2 a = 1 + tg 2 a 
 
05 
 
y = u.v 
 
y’ = uv´+ vu´ 
 
 
06 y = 
v
u
 y’ = 
2v
uv' - vu'
 
 
cossec 2 a = 1 + cotg 2 a 
07 
y = u m y’ = m.u
u'.1m
 
 
 
08 
 
y = 
m u
(m inteiro) 
y’ = 
m 1-mum
u'
 
 
sen2 a = 
2
2cos1 a
 
09 
y = a u (a > 0) y’ = a
u' . lnau
 
 
10 
y = e u y’ = e
 u' .u
 
 
 
11 
 
y = ln u y’ = 
u
u '
 
 
cos 2 a = 
2
2cos1 a
 
 
12 
 
y = log
a
u y’ = 
aln 
'
u
u
 
 
13 
y = u v (u > 0 ) 
y’ = 
sen 2a = 2 sen a . cos a 
 
14 
 
y = sen u 
 
y’ = cos u . u’ 
 
 
15 
 
y = cos u 
 
y’ = - sen u. u’ 
 
cos 2a = 1 – 2 sen 2 a 
 
16 
 
y = tg u 
 
y’ = sec 2 u . u’ 
 
 
17 
 
y = cotg u 
 
y’ = - cossec 2 u . u’ 
 
cos 2a = cos 2 a - sen2 a 
 
18 
 
y = sec u 
 
y’ = sec u . tg u . u’ 
 
 
19 
 
y = cossec u 
 
y’ = -cossec u. cotg u. u’ 
 
cos 2a = 2 cos 2 a - 1 
 
20 
 
y = arcsen u y’ = 
21
'
u
u

 
 
 
21 
 
y = arccos u y’ = - 
21
'
u
u

 
 sen(u + v) = sen u.cos v + cos u.sen v 
 
22 
 
y = arctg u y’ = 
21
'
u
u

 
 
 
23 
 
y = arccotg u y’ = - 
21
'
u
u

 
 
 
24 
 
y = arcsec u y’ = 
1
'
2 uu
u
 
 
25 y = arccossec u 
y’ = - 
1
'
2 uu
u
 
 
 
 Profa. Eliane Prezepiorski