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ÿÿÿÿ ã¹ÇÔªÒá¤Å¤ÙÅÑÊ ¡¯ÅÙ¡â«è (Íѧ¡ÄÉ: Chain rule) ¤×ÍÊÙµÃÊÓËÃѺ¡ÒÃËÒ͹ؾѹ¸ì¢Í§¿Ñ§¡ìªÑ¹¤ÍÁâ¾ÊÔµ
ÿÿÿÿ àËç¹ä´éªÑ´ÇèÒ ËÒ¡µÑÇá»Ã y à»ÅÕè¹á»Å§µÒÁµÑÇá»Ã u «Öè§à»ÅÕè¹á»Å§µÒÁµÑÇá»Ã x áÅéÇ ÍѵÃÒ¡ÒÃà»ÅÕè¹á»Å§¢Í§ y à·Õº¡Ñº x ËÒä´é¨Ò¡¼Å¤Ù³ ¢Í§ÍѵÃÒ¡ÒÃà»ÅÕè¹á»Å§¢Í§ y à·Õº¡Ñº u ¤Ù³¡Ñº ÍѵÃÒ¡ÒÃà»ÅÕè¹á»Å§¢Í§ u à·Õº¡Ñº x
ÿÿÿÿ ÊÁÁµÔãË餹˹Öè§»Õ¹à¢Ò´éÇÂÍѵÃÒ 0.5 ¡ÔâÅàÁµÃµèͪÑèÇâÁ§ ÍØ³ËÀÙÁÔ¨ÐÅ´µèÓŧàÁ×èÍÃдѺ¤ÇÒÁÊÙ§à¾ÔèÁ¢Öé¹ ÊÁÁµÔãËéÍѵÃÒà»ç¹ Ŵŧ 6 °F µèÍ¡ÔâÅàÁµÃ ¶éÒàÃÒ¤Ù³ 6 °F µèÍ¡ÔâÅàÁµÃ´éÇ 0.5 ¡ÔâÅàÁµÃµèͪÑèÇâÁ§ ¨Ðä´é 3 °F µèͪÑèÇâÁ§ ¡Òäӹdzàªè¹¹Õéà»ç¹µÑÇÍÂèÒ§¢Í§¡ÒûÃÐÂØ¡µìãªé¡®ÅÙ¡â«è
ÿÿÿÿ ã¹·Ò§¾Õª¤³Ôµ ¡®ÅÙ¡â«è (ÊÓËÃѺµÑÇá»Ãà´ÕÂÇ) ÃкØÇèÒ ¶éҿѧ¡ìªÑ¹ f ËÒ͹ؾѹ¸ìä´é·Õè g(x) áÅпѧ¡ìªÑ¹ g ËÒ͹ؾѹ¸ìä´é·Õè x ¤×ÍàÃÒ¨Ðä´é ´Ñ§¹Ñé¹
ÿÿÿÿ ¹Í¡¨Ò¡¹Õé ´éÇÂÊѡóì¢Í§äźì¹Ô« ¡®ÅÙ¡â«èà¢Õ¹᷹ä´é´Ñ§¹Õé:
ÿÿÿÿ àÁ×èÍ ÃкØÇèÒ f à»ÅÕè¹á»Å§µÒÁ g àËÁ×͹à»ç¹µÑÇá»Ã˹Öè§.
The general power rule
ÿÿÿÿ ¡®àŢ¡¡ÓÅѧ·ÑèÇä» ÊÒÁÒö¹ÓÁÒãªé¡Ñº¡®ÅÙ¡â«èä´é
Example I
¾Ô¨ÒÃ³Ò f(x) = (x2 + 1)3. f(x) à·Õºä´é¡Ñº h(g(x)) â´Â·Õè g(x) = x2 + 1 áÅÐ h(x) = x3 ´Ñ§¹Ñé¹
f'(x) |
= 3(x2 + 1)2(2x) |
|
= 6x(x2 + 1)2 |
Example II
㹡ÒÃËÒ͹ؾѹ¸ì¢Í§¿Ñ§¡ìªÑ¹µÃÕ⡳ÁÔµÔ
f(x) = sin(x2),
àÃÒÊÒÁÒöà¢Õ¹ f(x) = h(g(x)) ´éÇ h(x) = sinx áÅÐ g(x) = x2 ¨Ò¡¡®ÅÙ¡â«è ¨Ðä´é
f'(x) = 2xcos(x2)
à¹×èͧ¨Ò¡ h'(g(x)) = cos(x2) áÅÐ g'(x) = 2x
¡®ÅÙ¡â«èÊÓËÃѺËÅÒµÑÇá»Ã
ÿÿÿÿ ¡®ÅÙ¡â«èãªéä´é¡Ñº¿Ñ§¡ìªÑ¹ËÅÒµÑÇá»Ãàªè¹¡Ñ¹ µÑÇÍÂèÒ§àªè¹ ¶éÒàÃÒÁտѧ¡ìªÑ¹ f(u(x,y),v(x,y)) â´Â·Õè
u(x,y) = 3x + y2 áÅÐ v(x,y) = sin(xy)
´Ñ§¹Ñé¹
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