设函数fx=x(x-1)(x-2)……(x-100)求x=1的导数

问题描述:

设函数fx=x(x-1)(x-2)……(x-100)求x=1的导数

解函数fx=x(x-1)(x-2)……(x-100)
=(x-1)x(x-2)……(x-100)
则f'(x)=[(x-1)x(x-2)……(x-100)]'
=(x-1)'x(x-2)……(x-100)+(x-1)×[(x-1)x(x-2)……(x-100)]'
=1×x(x-2)……(x-100)+(x-1)×[(x-1)x(x-2)……(x-100)]'
即f'(x)=1×1*(1-2)……(x-100)+(1-1)×[(x-1)x(x-2)……(x-100)]'
=1×1*(1-2)……(x-100)+0×[(x-1)x(x-2)……(x-100)]'
=(-3)(-4)(-5).(-99)
=(-1)(-2)(-3)(-4)(-5).(-99)/(-1)(-2)
=-99!/2