作业帮求多项式的求导f(x)=x(x-1)(x-2)(x-3)(x-4)…………（x-1000)求f（x）的导数式,重赏.【要有具体过程,
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求多项式的求导f(x)=x(x-1)(x-2)(x-3)(x-4)…………（x-1000)求f（x）的导数式,重赏.【要有具体过程,
求多项式的求导
f(x)=x(x-1)(x-2)(x-3)(x-4)…………（x-1000)
求f（x）的导数式,重赏.【要有具体过程,
求多项式的求导f(x)=x(x-1)(x-2)(x-3)(x-4)…………（x-1000)求f（x）的导数式,重赏.【要有具体过程,
当成两个因式的乘积那样求导 具体方法如下
f'(x)=(x-1)(x-2)(x-3)(x-4)…………（x-1000)
+x(x-2)(x-3)(x-4)…………（x-1000)
+x(x-1)(x-3)(x-4)…………（x-1000)
+...+x(x-1)(x-2)(x-3)…………（x-999)
=x(x-1)(x-2)(x-3)(x-4)……（x-1000)[1/x+1/(x-1)+1/(x-2)+...+1/(x-1000)]
令g(x) = ln f(x) = lnx + ln(x-1) +……+ ln(x-1000)
g'(x) = f'(x)/f(x) = 1/x +1/(x-1) +……+ 1/(x-1000)
就有f'(x)/f(x) = 1/x +1/(x-1) +……+ 1/(x-1000)
把f(x)移到右边就行了
f'(x) = f(x) [1/x +1/(x-1) +…...
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令g(x) = ln f(x) = lnx + ln(x-1) +……+ ln(x-1000)
g'(x) = f'(x)/f(x) = 1/x +1/(x-1) +……+ 1/(x-1000)
就有f'(x)/f(x) = 1/x +1/(x-1) +……+ 1/(x-1000)
把f(x)移到右边就行了
f'(x) = f(x) [1/x +1/(x-1) +……+ 1/(x-1000)]
=x(x-1)(x-2)(x-3)(x-4)…………（x-1000)[1/x+1/(x-1)+1/(x-2)+...+1/(x-1000)]
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