设f(x)=(x-1)(x-2)……(x-n)/(x+1)(x+2)……(x+n),求导f'(1)我算的结果是(-1)^n/(n+1),
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![设f(x)=(x-1)(x-2)……(x-n)/(x+1)(x+2)……(x+n),求导f'(1)我算的结果是(-1)^n/(n+1),](/uploads/image/z/5909189-5-9.jpg?t=%E8%AE%BEf%28x%29%3D%28x-1%29%28x-2%29%E2%80%A6%E2%80%A6%28x-n%29%2F%28x%2B1%29%28x%2B2%29%E2%80%A6%E2%80%A6%EF%BC%88x%2Bn%29%2C%E6%B1%82%E5%AF%BCf%27%281%29%E6%88%91%E7%AE%97%E7%9A%84%E7%BB%93%E6%9E%9C%E6%98%AF%EF%BC%88-1%EF%BC%89%5En%2F%28n%2B1%29%2C)
设f(x)=(x-1)(x-2)……(x-n)/(x+1)(x+2)……(x+n),求导f'(1)我算的结果是(-1)^n/(n+1),
设f(x)=(x-1)(x-2)……(x-n)/(x+1)(x+2)……(x+n),求导f'(1)
我算的结果是(-1)^n/(n+1),
设f(x)=(x-1)(x-2)……(x-n)/(x+1)(x+2)……(x+n),求导f'(1)我算的结果是(-1)^n/(n+1),
(-1)^(n-1)/(n(n+1)),
f(x)=(x-1)(x-2)……(x-n)/(x+1)(x+2)……(x+n)
=(x-1)[(x-2)……(x-n)/(x+1)(x+2)……(x+n)]
=(x-1)'[(x-2)……(x-n)/(x+1)(x+2)……(x+n)]+(x-1)[(x-2)……(x-n)/(x+1)(x+2)……(x+n)]'
f(1)=(1-2)……(1-n)/(1+1)(1+...
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f(x)=(x-1)(x-2)……(x-n)/(x+1)(x+2)……(x+n)
=(x-1)[(x-2)……(x-n)/(x+1)(x+2)……(x+n)]
=(x-1)'[(x-2)……(x-n)/(x+1)(x+2)……(x+n)]+(x-1)[(x-2)……(x-n)/(x+1)(x+2)……(x+n)]'
f(1)=(1-2)……(1-n)/(1+1)(1+2)……(1+n)
=(-1)^(n-1)*1*2*...*(n-1)/2*3*...*(n+1)
=(-1)^(n-1)/(n(n+1)),
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