若f(x)=(x-1)(x-2)…(x-9)(x-10)则f'(10)=对于此题,有9!和0两种答案.能否给我一个清楚的过程,让我明白到底哪种对.
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若f(x)=(x-1)(x-2)…(x-9)(x-10)则f''(10)=对于此题,有9!和0两种答案.能否给我一个清楚的过程,让我明白到底哪种对.若f(x)=(x-1)(x-2)…(x-9)(x-10
若f(x)=(x-1)(x-2)…(x-9)(x-10)则f'(10)=对于此题,有9!和0两种答案.能否给我一个清楚的过程,让我明白到底哪种对.
若f(x)=(x-1)(x-2)…(x-9)(x-10)则f'(10)=
对于此题,有9!和0两种答案.能否给我一个清楚的过程,让我明白到底哪种对.
若f(x)=(x-1)(x-2)…(x-9)(x-10)则f'(10)=对于此题,有9!和0两种答案.能否给我一个清楚的过程,让我明白到底哪种对.
解法一:
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)]}'=1/(x-1)+1/(x-2)+……+1/(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)
把x=10代入,就求出f'(10)了.
解法二:
设y=(x-1)(x-2)……(x-9)
则:f(x)=y(x-10),
f'(x)=(x-10)y'+y(x-10)'=(10-x)y'+y
则:f'(x)|10=(10-10)y'+y=9!
即:f'(10)=9!
f(x)=(x-1)(x-2)…(x-9)(x-10)
设g(x)=(x-1)(x-2)………(x-9)
f(x)=g(x)(x-10)
f'(x)=g'(x)(x-10)+g(x)
f'(10)=0+g(10)
所以
f'(10)=(10-1)(10-2)…………(10-9)
=9!
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