Question

导数问题 求解答 求帮助 求指教 谢谢啦！！！

Answer 1

ƒ(x) = x(x - 1)(x - 2) ... (x - 100)
ƒ'(x) = x'(x - 1)(x - 2) ... (x - 100) + x(x - 1)'(x - 2) ... (x - 100) + ... + x(x - 1)(x - 2) ... (x - 100)'
= (x - 1)(x - 2) ... (x - 100) + x(x - 2) ... (x - 100) + ... + x(x - 1)(x - 2) ... 1
ƒ'(0) = (- 1)(- 2) ... (- 100) + 0 +... + 0
= 1 * 2 * 3 * 4 * ... * 100
= 100 * 99 * 98 * ... * 2 * 1

Answer 2

f(x)=x(x-1)(x-2)...(x-100)
f'(x) =(x-1)(x-2)...(x-100)+x(x-2)...(x-100)+x(x-1)(x-3)...(x-100)+...x(x-1)(x-2)...(x-99)
f'(0) =(0-1)(0-2)...(0-100)
=100!
Ans :D