设f(x)=x(x+1)(x+2)…(x+n),则f''(0)=_____.
n! 解析: 设g(x)=(x+1)(x+2)…(x+n),则f(x)=xg(x),于是f''(x)=g(x)+ xg''(x),所以f''(0)=g(0)+0•g''(0)一g(0)=1•2•…•n=n!.
设f(x)=x(x+1)(x+2)…(x+n),则f''(0)=_____.
n! 解析: 设g(x)=(x+1)(x+2)…(x+n),则f(x)=xg(x),于是f''(x)=g(x)+ xg''(x),所以f''(0)=g(0)+0•g''(0)一g(0)=1•2•…•n=n!.