求y=(x-1)(x-2)(x-3)...（x-10)（x大于10）的导数.详细过程_数学解答

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

人气：316 ℃　时间：2019-08-16 20:05:08

解答

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)