设f(x)==x(x-1).(x-100),则f(50)的导数是多少

Question

设f(x)==x(x-1).(x-100),则f(50)的导数是多少

Answer 1

把f(x)看成下面两个函数的乘积
f(x)=[x(x-1)...(x-49)(x-51)...(x-100)](x-50)
f‘(x)=[x(x-1)...(x-49)(x-51)...(x-100)]’ (x-50)
+[x(x-1)...(x-49)(x-51)...(x-100)]
所以：
f‘(50)=[50(50-1)...(50-49)(50-51)...(50-100)]
=(50!)^2