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,
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 04:49:05
![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,](/uploads/image/z/7808393-65-3.jpg?t=%E6%B1%82%E5%A4%9A%E9%A1%B9%E5%BC%8F%E7%9A%84%E6%B1%82%E5%AF%BCf%28x%29%3Dx%28x-1%29%28x-2%29%28x-3%29%28x-4%29%E2%80%A6%E2%80%A6%E2%80%A6%E2%80%A6%EF%BC%88x-1000%29%E6%B1%82f%EF%BC%88x%EF%BC%89%E7%9A%84%E5%AF%BC%E6%95%B0%E5%BC%8F%2C%E9%87%8D%E8%B5%8F.%E3%80%90%E8%A6%81%E6%9C%89%E5%85%B7%E4%BD%93%E8%BF%87%E7%A8%8B%2C)
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) +…...
全部展开
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)]
收起