Question

求y=(x-1)(x-2)(x-3)...（x-10)（x大于10）的导数.

Answer 1

f(x)=(x-1)(x-2)……(x-10),

ln[f(x)]=ln[(x-1)(x-2)……(x-10)]

ln[f(x)]=ln(x-1)+ln(x-2)+……+ln(x-10)

{ln[f(x)]}'=[ln(x-1)+ln(x-2)+……+ln(x-10)]'

f'(x)/f(x)=1/(x-1)+1/(x-2)+……+1/(x-10)

f'(x)=[1/(x-1)+1/(x-2)+……+1/(x-10)]f(x)