4.6 Differentiation by rule 109
EXAMPLE 4.17Inverse trig functions
If thenx 1 = 1 a 1 sin 1 yand
If yhas its principal value then it lies between and and cos yis positive.
Then
and
0 Exercises 60 – 62
The derivatives of the inverse hyperbolic functions (Section 3.9) are given in
Table 4.6.
dy
dx
ax
=
−
1
22aya yaa yaxcos =− =− 1 sin sin =−
222222π
2
− ,
π
2
dx
dy
ay
dy
dx a y
=, =cos
cos
1
y
x
a
=
−sin
1Table 4.5
d
dx
x
a
a
ax
tan
−
=
1
22
d
dx
x
a
ax
cos
−
=
−
−
1
22
1
d
dx
x
a
ax
sin
−
=
−
1
22
1
Table 4.6
d
dx
x
a
a
ax
tanh
−
=
−
1
22
d
dx
x
a
xa
cosh
−
=
−
1
22
1
d
dx
x
a
xa
sinh
−
=
1
22
1