f(x)=x(x-1)(x-2)…(x-100),求f'(100).

f(x)=x(x-1)(x-2)…(x-100),求f'(100).
f(x)=x(x-1)(x-2)…(x-100),求f'(100).

f(x)=x(x-1)(x-2)…(x-100),求f'(100).
f(x)=x(x-1)(x-2)……(x-100)两边取对数得.lnf(x)=lnx+ln(x-1)+ln(x-2)+……+ln(x-1).两边求导数得.f'(x)/f(x)=1/x+1/(x-1)+1/(x-2)+……+1/(x-100).所以.f'(x)=f(x)[1/x+1/(x-1)+1/(x-2)+……+1/(x-100)……（*）.=(x-1)(x-2)……(x-100)+x(x-2)……(x-100)+x(x-1)……(x-100)+……+x(x-1)(x-2)……(x-99)
把x=100带入的出结果

楼上过程没问题，我是从定义走的，给予一下借鉴吧

f(x)=x(x-1)(x-2)…(x-99)(x-100),求f'(100) f(x)=x^2+x (x f(x)={2x+1,x f(x)={1+x/2,x f(x)=(x-1)/(x+2) f(x)=x(x-1)(x+2)(x-3)(x+4)……(x+100),求f'(1) f(x)+f((x-1)/x)=2x; x!=0,1; 求f(x) f(x)+f[(x-1)/x]=2x x不等于0,1.求f(x). max{f(x),g(x)}=1/2(f(x)+g(x)+|f(x)-g(x)| 设f(x)=x(x-1)(x-2)……(x-100)求,f'(1) f(x)=x(x-1)(x-2)…(x-99),怎么求f'(0)=? 已知f(x)=(x-1)(x-2)(x-3)…(x-2008),求f’(1). f(x)=x(x-1)(x-2)…(x-100),求f'(100). f(X)=f(X+2)(x 函数F(x)=2x,x>=1,F(x)=x^2,x f(x)=|x+2|+|x-2|值域 f(x)=|x-2|-|x+1|值域 已知f(x+1/x)=x^2+1/x^2+1/x则f(x) 设2f(x)+xf(1/x)=(x+2x)/(x+1),求f(x).