1. The derivative of sen(arcsen(x)) is 1/√(1-x^2). 2. The derivative of cos(arccos(x)) is -1/√(1-x^2). 3. The derivative of a function involves applying the chain rule and adding/subtracting terms involving derivatives of nested functions.

1. Regras de Diferenciação
1 ( ) 0c
dx
d
= 19 2
x1
1
)x(senarc
dx
d
−
=
2 ( )[ ] ( )x'fcxfc
dx
d
= 20 2
x1
1
)xcos(arc
dx
d
−
−=
3 ( ) ( )[ ] ( ) ( )x'gx'fxgxf
dx
d
+=+ 21 2
x1
1
)x(tgarc
dx
d
+
=
4 ( ) ( )[ ] ( ) ( )x'gx'fxgxf
dx
d
−=− 22
1xx
1
)xsec(cosarc
dx
d
2
−
−=
5 ( ) ( )[ ] ( ) ( ) ( ) ( )x'gxfxgx'fxgxf
dx
d
+= 23
1xx
1
)xsec(arc
dx
d
2
−
=
6
( )
( )
( ) ( ) ( ) ( )
( )[ ]2
xg
x'gxfxgx'f
xg
xf
dx
d −
=





24 2
x1
1
)x(gcotarc
dx
d
+
−=
7 )x('g))x(g('f))x(g(f
dx
d
= 25 )xcosh()x(senh
dx
d
=
8
1nn
xn)x(
dx
d −
= 26 )x(senh)xcosh(
dx
d
=
9
xx
e)e(
dx
d
= 27 )x(hsec)x(tgh
dx
d 2
=
10 )aln(a)a(
dx
d xx
= 28 )x(ghcot)x(hseccos)x(hseccos
dx
d
−=
11
x
1
xln
dx
d
= 29 )x(tgh)x(hsec)x(hsec
dx
d
−=
12
)aln(x
1
)x(log
dx
d
a = 30 )x(hseccos)x(ghcot
dx
d 2
−=
13 )xcos()x(sen
dx
d
= 31 2
x1
1
)x(senharc
dx
d
+
=
14 )x(sen)xcos(
dx
d
−= 32
1x
1
)xcosh(arc
dx
d
2
−
=
15 )x(sec)x(tg
dx
d 2
= 33 2
x1
1
)x(tgharc
dx
d
−
=
16 )xcot()xsec(cos)xsec(cos
dx
d
−= 34
1xx
1
)x(hseccosarc
dx
d
2
+
−=
17 )x(tg)xsec()xsec(
dx
d
= 35 2
x1x
1
)x(hsecarc
dx
d
−
−=
18 )x(seccos)x(gcot
dx
d 2
−= 36 2
x1
1
)x(ghcotarc
dx
d
−
=