Solution 9.10.3.6
S
G
a
=
a
G
@G
@a
=
a
abK
(s + a)(s+ b)
@
@a
abK
s
2
+(a + b)s + ab
=
s
2
+(a+ b)s + ab
bK
;ab(s + b)K
(s
2
+(a + b)s + ab)
2
+
bK
s
2
+(a+ b)s+ ab
= s
2
+(a + b)s + ab
;a(s + b)
(s
2
+(a + b)s+ ab)
2
+
1
s
2
+(a+ b)s+ ab
= s
2
+(a + b)s + ab
"
;as;ab+ s
2
+(a + b)s + ab
(s
2
+(a+ b)s + ab)
2
#
=
s(s + b)
s
2
+(a+ b)s + ab
:
T
c
(s) =
abK
s
2
+(a + b)s + ab
1+
abK
s
2
+(a + b)s + ab
=
abK
s
2
+(a+ b)s +(ab+ abK)
:
S
T
c
a
=
a
T
c
@T
c
@a
=
a
abK
s
2
+(a+ b)s + ab(1 + K)
@
@a
abK
s
2
+(a + b)s + ab(1 + K)
=
s
2
+(a+ b)s + ab(1 + K)
bK
;abK[s + b(1 + K)]
[s
2
+(a+ b)s + ab(1 + K)]
2
+
bK
s
2
+(a + b)s+ ab(1 + K)
= s
2
+(a + b)s + ab(1 + K)
;a[s + b(1 + K)]
[s
2
+(a + b)s + ab(1 + K)]
2
+
1
s
2
+(a + b)s+ ab(1 + K)
= s
2
+(a + b)s + ab(1 + K)
"
;as;ab(1 + K)+s
2
+(a + b)s + ab(1 + K)
[s
2
+(a + b)s + ab(1 + K)]
2
#
=
s(s + b)
s
2
+(a+ b)s + ab(K +1)
S
G
K
=
K
G
@G
@K
=
K
abK
(s + a)(s+ b)
@
@K
abK
s
2
+(a + b)s + ab
=
s
2
+(a+ b)s + ab
ab
ab
(s
2
+(a + b)s + ab)
= 1
S
T
c
K
=
K
T
c
@T
c
@K
=
K
abK
s
2
+(a+ b)s + ab(1 + K)
@
@K
abK
s
2
+(a + b)s + ab(1 + K)
=
s
2
+(a+ b)s + ab(1 + K)
ab
;abK(ab)
[s
2
+(a+ b)s + ab(1 + K)]
2
+
ab
s
2
+(a + b)s+ ab(1 + K)
= s
2
+(a + b)s + ab(1 + K)
;abK
(s
2
+(a + b)s + ab(1 + K))
2
+
1
s
2
+(a+ b)s+ ab(1 + K)
= s
2
+(a + b)s + ab(1 + K)
"
;abK + s
2
+(a+ b)s + ab + abK)
(s
2
+(a + b)s + ab(1 + K))
2
#
=
s
2
+(a + b)s+ ab
s
2
+(a+ b)s + ab(K +1)