Tabela de Derivada

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FUNÇÃO DERIVADA FUNÇÃO DERIVADA 
1 y = c y' = 0 21 y = arc tg u 
 
2 y = x y' = 1 22 y = arc cotg u 
 
3 y = cu y' = cu' 23 y = arc cosec u, 
 
4 y = u ± v ± w y' = u' ± v' ± w’ 24 y = arc sec u, 
 
5 y = uv y' = u'v + uv' 25 y = senh u ucosh'.u'y = 
6 
 
 
26 y = cosh u usenh'u'y = 
7 nuy =
 
'uu.n'y n 1−=
 
27 y = tgh u usech'.u'y 2=
 
8 ( )10 ≠<= aay u
 
aln.a'.u'y u=
 
28 y = cotgh u ucosech'.u'y 2−=
 
9 uey =
 
ue'.u'y =
 
29 y = sech u tghu.usech'.u'y −= 
10 ulogy a= 
a.lnu
'u
'y =
 
30 y = cosech u ucotgh.ucosech'.u'y −= 
11 y = uv (u > 0) 
 
31 y = arg senh u 
 
12 y = ln u 
 
32 y = arg cosh u 
, u > 1 
13 y = sen u ucos'.u'y = 33 y = arg tgh u 
, |u| < 1 
14 y = cos u senu'.u'y −= 34 y = arg cotgh u 
, |u| > 1 
15 y = tg u usec'.u'y 2=
 
35 y = arg sech u 
, 0 < u < 1 
16 y = sec u tgu.usec'.u'y = 36 y = arg cosech u 
, 
17 y = cotg u ueccos'.u'y 2−=
 
37 
( )[ ]
( )[ ]'tx
'ty
dx
dy
=
 
18 y = cosec u gucot.ecucos'.u'y −= 
19 y = arc sen u 
 
 
 
20 y = arc cos u