Question

数学f(x)=x(x+1)(x+2)(x+3)(x+4)(x+5),求f'(0)=???

Answer 1

f ’ （x）=x' * (x+1)(x+2)(x+3)(x+4)(x+5)+x * {(x+1)(x+2)(x+3)(x+4)(x+5)}'
当x=0时
f ' (0)=1*(x+1)(x+2)(x+3)(x+4)(x+5) + 0 * {(x+1)(x+2)(x+3)(x+4)(x+5)}
=(x+1)(x+2)(x+3)(x+4)(x+5)=1*2*3*4*5=5!=120

Answer 2

f'(x)=(x+1)(x+2)(x+3)(x+4)(x+5)+x(x+2)(x+3)(x+4)(x+5)+x(x+1)(x+3)(x+4)(x+5)+x(x+1)(x+2)(x+4)(x+5)+x(x+1)(x+2)(x+3)(x+5)+x(x+1)(x+2)(x+3)(x+4),
f'(0)=1*2*3*4*5+0+0+0+0+0=120