Solution 9.10.3.2
S
G
a
=
a
G
@G
@a
=
a
Ka
s+ a
@
@a
Ka
s +a
=
s+ a
K
;aK
(s+ a)
2
+
K
s+a
= (s+a)
s+a;a
(s+a)
2
=
s
(s+a)
S
T
c
a
=
a
T
c
@T
c
@a
=
a
Ka
s+(K + a)
@
@a
Ka
s+ K +a
=
s+ a+K
K
;Ka
Ks+K + a)
2
+
K
s+K + a
= (s+a)
;a+s +K + a
(s +K +a)
2
=
(s+K)
(s+K + a)
S
G
K
=
K
G
@G
@K
=
K
Ka
s+ a
@
@K
Ka
s+ a
=
(s+a)
a
a
s+ a
= 1:
S
T
c
K
=
K
T
c
@T
c
@a
=
K
Ka
s+ K +a
@
@K
Ka
s+K + a
=
s+ K +a
a
;Ka
(s+K +a)
2
+
a
s +K + a
=
s+ K +a
a
;K +s +K +a
(s+ K +a)
2
=
s+a
s+ K +a