(1/2)设f(x)＝x(x+1)(x+2)···(x+100),求f'(0) .这道题应该用导数的定义来做,但是我算不出一...(1/2)设f(x)＝x(x+1)(x+2)···(x+100),求f'(0) .这道题应该用导数的定义来做,但是我算不出一个确切的值,

(1/2)设f(x)＝x(x+1)(x+2)···(x+100),求f'(0) .这道题应该用导数的定义来做,但是我算不出一...(1/2)设f(x)＝x(x+1)(x+2)···(x+100),求f'(0) .这道题应该用导数的定义来做,但是我算不出一个确切的值,
(1/2)设f(x)＝x(x+1)(x+2)···(x+100),求f'(0) .这道题应该用导数的定义来做,但是我算不出一...
(1/2)设f(x)＝x(x+1)(x+2)···(x+100),求f'(0) .这道题应该用导数的定义来做,但是我算不出一个确切的值,

(1/2)设f(x)＝x(x+1)(x+2)···(x+100),求f'(0) .这道题应该用导数的定义来做,但是我算不出一...(1/2)设f(x)＝x(x+1)(x+2)···(x+100),求f'(0) .这道题应该用导数的定义来做,但是我算不出一个确切的值,
很简单设g(x)=(x+1)(x+2)···(x+100)
f(x)=xg(x) f'(x)=g(x)+xg'(x)
f'(0)=g(0)+0*g'(x)=g(0)
=1*2*3*...*100
=100!

f'(0)=【f(x)-f(0)]/(x-0){x趋向于0时的极限}
=(x+1)(x+2)...(x+100){x趋向于0时的极限}
=(0+1)(0+2)....(0+100)
=100的阶乘