问题标题：
【求解数学题：f(x)=x^5*exp(x^2)showf'(x)=2007!/1001!一道微分证明题,急!provef(2007)(0)=2007!/1001!notf'(x)=2007!/1001!i.e.the2007thderivativeoff(x)equals2007!/1001!whenx=0】
问题描述：
求解数学题：f(x)=x^5*exp(x^2)showf'(x)=2007!/1001!
一道微分证明题,急!
provef(2007)(0)=2007!/1001!notf'(x)=2007!/1001!
i.e.the2007thderivativeoff(x)equals2007!/1001!whenx=0
杜文莉回答：
f(x)=x^5*exp(x^2)
用泰勒级数展开exp(x^2)然后再乘以x^5
exp(x^2)
=1+x^2/1!+x^4/2!+x^6/3!+...+x^2002/1001!+.
f(x)
=x^5*exp(x^2)
=x^5+x^7/1!+x^9/2!+x^11/3!+...+x^2007/1001!+.
x^2007项的系数=f(2007)(0)/2007!=1/1001!
故f(2007)(0)=2007!/1001!
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