Chapter 3 9 8.Derivative of Matrix Function p11(t) dP0=P(0≌ p2(0… pim(t) dt p.2(t) Pnm(t)】 In a similar way ) df()-f0= f5(0) dt U 9.The gradient of f(X）f:R"→R af(x) Ox f(x) af(x) OX Ox2 Notations:Vf(X)or grad f(X)or f(x) Ox Example: 7 2X1 f(X)=f(x2 )=x2+sin x,+e" Then VI= ar coSX2 OX8. Derivative of Matrix Function             ( ) ( ) ... ( ) ... ... ... ... ( ) ( ) ... ( ) ( ) ( ) 1 2 1 1 1 2 1 p t p t p t p t p t p t t d t d t n n n m m       P P In a similar way                  ( ) ... ( ) ( ) ( ) ( ) 2 1 f t f t f t t dt d t n    f f 9. The gradient of f ( X ) f R R n :                                n x f x f x f f ( ) ... ( ) ( ) ( ) 2 1 X X X X X Notations: or or  f ( X ) g r a d f ( X ) X f Example: 3 2 2 1 3 2 1 ( ) ( ) sin x x x e x x x f f              X  Then                3 2 1 cos 2 x e x x f f X Chapter 3 9