Ť

١

ԪŤ ١ (ѧ: Chain rule) ٵѺ͹ؾѹͧѧѹԵ

Ѵ ҡ y ¹ŧ u ¹ŧ x ѵҡ¹ŧͧ y ºѺ x ҡŤٳ ͧѵҡ¹ŧͧ y ºѺ u ٳѺ ѵҡ¹ŧͧ u ºѺ x

餹˹觻չҴѵ 0.5 õͪ سŴŧдѺ٧ ѵ Ŵŧ 6 °F ͡ Ҥٳ 6 °F ͡ô 0.5 õͪ 3 °F ͪ äӹdz蹹繵ҧͧûء顮١

㹷ҧժԵ ١ (Ѻ) к ҿѧѹ f ͹ؾѹ g(x) пѧѹ g ͹ؾѹ x Ҩ ѧ

͡ҡ ѭóͧźԫ ١¹᷹ѧ:

к f ¹ŧ g ͹繵˹.

The general power rule

Ţ¡ѧöѺ١

Example I

Ԩó f(x) = (x2 + 1)3. f(x) ºѺ h(g(x)) · g(x) = x2 + 1 h(x) = x3 ѧ

f'(x)

= 3(x2 + 1)2(2x)

= 6x(x2 + 1)2

Example II

㹡͹ؾѹͧѧѹ⡳Ե

f(x) = sin(x2),

ö¹ f(x) = h(g(x)) h(x) = sinx g(x) = x2 ҡ١

f'(x) = 2xcos(x2)

ͧҡ h'(g(x)) = cos(x2) g'(x) = 2x

١Ѻµ

١Ѻѧѹµ蹡ѹ ҧ տѧѹ f(u(x,y),v(x,y)) ·

u(x,y) = 3x + y2 v(x,y) = sin(xy)

ѧ

٨졮١

f g 繿ѧѹ x 繨ӹǹ f ö͹ؾѹ g(x) g ͹ؾѹ x ѧ ҡͧ͹ؾѹ

з

㹷ӹͧǡѹ

з


١鹰ҹ

١繤سѵԾ鹰ҹͧͧ͹ؾѹ E F G ԺҹҤ (件֧٤Դ) f: E F g: F G 繿ѧѹ ж x Ҫԡͧ E f ͹ؾѹ x g ͹ؾѹ f(x) ͹ؾѹ (͹ؾѹવ) ͧѧѹԵ g o f x 繴ѧ

ѧࡵ͹ؾѹŧԧ Ţ ҡŧԧ᷹ԡ (¹ԡ) ҧҹҨС繡äٳԡ

á˹١ѴਹöҡԸշ繷ҡش M N P Ŵ Ck (ͺҹҤŴ)

f: M N g: N P

繡ŧ͹ؾѹ ͹ؾѹͧ fdf 繡ŧҡʢͧ M ѧʢͧ N ö¹᷹

Ըչ ٻẺͧ͹ؾѹлʨж١ͧٻѧ Category ͧŴ C աŧ C ѳҹ

http://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%8E%E0%B8%A5%E0%B8%B9%E0%B8%81%E0%B9%82%E0%B8%8B%E0%B9%88

ٻҾǢͧ

Ԫ


ͧṹ ?

ҧ :


Romeo

ʶҹ :
áҧ