M2 微分問題chain rule

chain rule 就即係層層d, 由外d到內,
而take limit係最正宗的prove,
因為我地學微分時, 根本就係用 limit 去 prove,

e.g. y = x^2
dy/dx = lim(h->0) [(x+h)^2 - x^2] / h
= lim(h->0) [x^2+2xh+h^2 -x^2 ] / h
= lim(h->0) (2x+h^2)
= 2x

你將個dx 乘番去右手邊
就即係 dy = 2x dx

如果將 y 變成 u^2,
dy 都係 = 2u du, 不過你可以左右除dx 呢個變數
變成 dy/dx = 2u du/dx, 就變成好似一條 chain rule 咁

其實我想講, 出到去公開試100%唔會考你prove chain rule,
只係你一定要記得有chain rule呢樣野,
有時你要d既野係 { cos [ e^(3x) ] }^3 呢d野就真係要層層d佢,

不過你真係好有興趣想知既話,可以搵我的 :)
因為對考試絕對唔會有用,
希望幫到你 :)

冇錯~I mean this

chain rule is dy/dx=(dy/du)(du/dx)

do u mean this?

2011-08-31 22:13:34 補充：
which part of the prove dont u understand??

2011-09-01 19:21:10 補充：
or u think is 唔嚴謹?