求分段函数的导数设 g(x)/x =0 f(x)={ 0 x=0 g(0)=g'(0)=0 g"(0)=2求 f‘（0）
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f(x)=g(x)/x,x!=0;f(x)=o,x=0

g(x)在x=0的Taylor展开式为个g(x)=g(0)+g'(0)x+g"(0)x^2/2!+O(x^2)

f'(0)=lim(x->0)[(f(x)-f(0))/(x-0)]

=lim(x->0)f(x)/x

=lim(x->0)g(x)/x^2

=lim(x->0)[g(0)+g'(0)x+g"(0)x^2/2!+O(x^2)] /x^2

代入 g(0)=g'(0)=0 ,g"(0)=2,

=1

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