高数题y=x(x-1)(x-2)(x-3).(x-99)(x-100) 求y‘(对y求导)?y=x(x-1)(x-2)(x-3).(x-99)(x-100) 求y‘(对y求导)?上头不对应该是f(x)=x(x-1)(x-2)(x-3)......(x-99)(x-100) 求f‘(0)=?
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![高数题y=x(x-1)(x-2)(x-3).(x-99)(x-100) 求y‘(对y求导)?y=x(x-1)(x-2)(x-3).(x-99)(x-100) 求y‘(对y求导)?上头不对应该是f(x)=x(x-1)(x-2)(x-3)......(x-99)(x-100) 求f‘(0)=?](/uploads/image/z/7015814-62-4.jpg?t=%E9%AB%98%E6%95%B0%E9%A2%98y%3Dx%28x-1%29%28x-2%29%28x-3%EF%BC%89.%EF%BC%88x-99%EF%BC%89%EF%BC%88x-100%EF%BC%89+%E6%B1%82y%E2%80%98%EF%BC%88%E5%AF%B9y%E6%B1%82%E5%AF%BC%EF%BC%89%3Fy%3Dx%28x-1%29%28x-2%29%28x-3%EF%BC%89.%EF%BC%88x-99%EF%BC%89%EF%BC%88x-100%EF%BC%89+%E6%B1%82y%E2%80%98%EF%BC%88%E5%AF%B9y%E6%B1%82%E5%AF%BC%EF%BC%89%3F%E4%B8%8A%E5%A4%B4%E4%B8%8D%E5%AF%B9%E5%BA%94%E8%AF%A5%E6%98%AFf%EF%BC%88x%EF%BC%89%3Dx%28x-1%29%28x-2%29%28x-3%EF%BC%89......%EF%BC%88x-99%EF%BC%89%EF%BC%88x-100%EF%BC%89+%E6%B1%82f%E2%80%98%EF%BC%880%EF%BC%89%3D%EF%BC%9F)
高数题y=x(x-1)(x-2)(x-3).(x-99)(x-100) 求y‘(对y求导)?y=x(x-1)(x-2)(x-3).(x-99)(x-100) 求y‘(对y求导)?上头不对应该是f(x)=x(x-1)(x-2)(x-3)......(x-99)(x-100) 求f‘(0)=?
高数题y=x(x-1)(x-2)(x-3).(x-99)(x-100) 求y‘(对y求导)?
y=x(x-1)(x-2)(x-3).(x-99)(x-100) 求y‘(对y求导)?
上头不对应该是
f(x)=x(x-1)(x-2)(x-3)......(x-99)(x-100) 求f‘(0)=?
高数题y=x(x-1)(x-2)(x-3).(x-99)(x-100) 求y‘(对y求导)?y=x(x-1)(x-2)(x-3).(x-99)(x-100) 求y‘(对y求导)?上头不对应该是f(x)=x(x-1)(x-2)(x-3)......(x-99)(x-100) 求f‘(0)=?
f‘(x)=(x-1)(x-2)(x-3).(x-99)(x-100)+x(x-2)(x-3).(x-99)(x-100)+x(x-1)(x-3).(x-99)(x-100)+……+x(x-1)(x-2)(x-3).(x-99),凡是含有x的项代入0之后都为0,只剩下第一项,所以f‘(0)=(-1)(-2)(-3).(-99)(-100)=[(-1)^100](100!)=100!(即100的阶乘)
f'(0)=100!
把对每个因式求导后的表达式看作一项,
结果等于所有表达式的和,
只有对x求导后的结果不为0,
其余项因为有x,结果都是0,
∴最后结果是:把0带入后1*2*3*...100=100!
用最原始的求导公式,f'(0) = lim [f(x) - f(0)] / x