f(x)=(x-a)(x-b)(x-c),则a/f^(a)+b/f^(b)+c/f^(c)=?
问题描述：
f(x)=(x-a)(x-b)(x-c),则a/f^(a)+b/f^(b)+c/f^(c)=?
答
∵f′(x)=(x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)∴f′(a)=(a-b)(a-c),f'(b)=(b-a)(b-c),f'(c)=(c-a)(c-b),代入得a/(a-b)(a-c)+b/(b-a)(b-c)+c/(c-a)(c-b) =[a(b-c)-b(a-c)+c(a-b)] / [(a-b)(a-c)(b-c)] = 0