Solution 9.10.3.1 S G a = a G @G @a = a a s + a @ @a a s + a = s + a 1  ;a (s + a) 2 + 1 s + a  = (s + a)  s + a;a (s + a) 2  = s (s + a) S T c a = a T c @T c @a = a a s +2a @ @a a s +2a = s +2a 1  ;2a (s +2a) 2 + 1 s +2a  = (s + a)  s +2a;2a (s +2a) 2  = s (s +2a) S G K = a G @G @K = K a s + a @ @K a s + a = K(s + a) a 0 = 0;; since there is no dependence on K: S T c K = a T c @T c @a = K a s +2a @ @K a s +2a = K(s +2a) a 0 = 0;; since there is no dependence on K: