(x+1)(x+2)·······(x+100)求f'(-2)
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(x+1)(x+2)·······(x+100)求f''(-2)(x+1)(x+2)·······(x+100)求f''(-2)(x+1)(x+2)·······(x+100)求f''(-2)-98!先按因
(x+1)(x+2)·······(x+100)求f'(-2)
(x+1)(x+2)·······(x+100)求f'(-2)
(x+1)(x+2)·······(x+100)求f'(-2)
-98!
先按因式分开求导为 (x+2)(x+3).(x+100)+(x+1)(x+3)(x+4)...(x+100)+.(x+1)(x+2)...(x+99)
除去第二个 别的式中都有因式(x+2)所以 带入-2 他们都是0 只剩下第二个式子不是0 所以结果就是 (-1)*1*2*3*4.*98=-98!(负98的阶乘)
f' = (x+2)(x+3)...(x+100) + (x+1)(x+3)...(x+100) + ...
即每一项为 f 分别除去x+1, x+2, x+3,...一共100项
f'(-2)中除了第二项(x+1)(x+3)...(x+100)以外,皆含有因数 x+2 = 0,所以那99项都是0
因此f'(-2) = (-2+1)(-2+3)(-2+4)...(-2+100) = -98!
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