Solution 9.10.3.10 S G a = a G @G @a = a Ka 2 (s + a) 2 @ @a Ka 2 (s + a) 2 = (s + a) 2 aK " ;a 2 K(2s+2a) (s 2 +2as + a 2 ) 2 + 2aK s 2 +2as + a 2 # = (s 2 +2as + a 2 ) " ;a(2s +2a)+2(s 2 +2as + a 2 ) (s 2 +2as + a 2 ) 2 # = 2s(s + a) (s + a) 2 = 2s (s + a) S T c a = a T c @T c @a = a a 2 K s 2 +2as + a 2 (K +1) @ @a a 2 K s 2 +2as + a 2 (K +1) = s 2 +2as + a 2 (K +1) aK " ;a 2 K(2s +2aK) [s 2 +2as + a 2 (K +1)] 2 + 2aK s 2 +2as + a 2 (K +1) # = s 2 +2as + a 2 (K +1 " ;a(2s +2aK)+2[s 2 +2as + a 2 (K + 1)] [s 2 +2as + a 2 (K +1)] 2 # = 2s 2 +2as ++2a 2 s 2 +2as + a 2 (K +1) S G K = K G @G @K = K Ka 2 (s + a) 2 @ @K Ka 2 (s + a) 2 = (s + a) 2 a 2 " a 2 (s + a) 2 # = 1 S T c K = K T c @T c @K = K a 2 K s 2 +2as + a 2 (K +1) @ @K a 2 K s 2 +2as + a 2 (K +1) = s 2 +2as + a 2 (K +1) a 2 " ;a 4 K [s 2 +2as + a 2 (K +1)] 2 + a 2 s 2 +2as + a 2 (K +1) # = s 2 +2as + a 2 (K +1) " ;a 2 K +[s 2 +2as + a 2 (K + 1)] [s 2 +2as + a 2 (K +1)] 2 # = s 2 +2as + a 2 s 2 +2as + a 2 (K +1) :