推 otzro :感謝!幫了我大忙 07/18 22:28
※ 引述《otzro (OTZro)》之銘言:
: 不好意思請問一下
: http://mykomica.org/boards/shieiuping/math/src/1310992759611.png
: 這題怎麼解
: 討論很久想不出來討論很久想不出來討論很久想不出來第二題怎麼解
: 第一題會解了(用題目直接微分)
f(ab) = f(a) + f(b) => f(1) = 0 and g(0) = 1
let a = g(u), b = g(v)
f(g(u)g(v)) = u + v
g(u)g(v) = g(u + v)
lim (g(x+h) - g(x))/h = lim g(x)(g(h)-1)/h
h->0 h->0
= g(x) lim (g(h)-1)/h (g(h) - 1 = 0 and h = 0 when h -> 0)
h->0
= g(x) lim g'(h) = g(x) g'(0) = g'(x)
h->0
g'(f(x)) f'(x) = 1
g(f(x)) g'(0) f'(x) = 1
x f'(x) = 1 / g'(0)
x f'(x) g'(x) = g(x) g'(0) / g'(0) = g(x)
記得考慮每一條式子 x 的範圍
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