Re: [微分] 幫我一下

[cipherman (雨云無日晴)]

※ 引述《terry1122 (我會一直守候著你)》之銘言：
: 設  g(x)=x*f(x)+1 ,  g(x+y)=g(x)*g(y) 且 lim f(x) = f(0)
:                                          x->0
: 求 g'(x)=

g'(x) = lim  [g(x+h)-g(x)]/h
        h->0

      = lim [g(x)(g(h)-1)]/h
        h->0

      = g(x) lim [g(h)-1]/h
             h->0

      = g(x) lim [(h*f(h)+1)-1]/h
             h->0

      = g(x) lim f(h)
             h->0

      = g(x)f(0)


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