设函数f(x)=(x-1)(x-2)(x-3)(x-4)(x-5),求导:f(1),f(3),f(x)的5阶导数及8阶导数,请问各位同仁怎么求啊?
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![设函数f(x)=(x-1)(x-2)(x-3)(x-4)(x-5),求导:f(1),f(3),f(x)的5阶导数及8阶导数,请问各位同仁怎么求啊?](/uploads/image/z/5348698-34-8.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3D%28x-1%29%28x-2%29%28x-3%29%28x-4%29%28x-5%29%2C%E6%B1%82%E5%AF%BC%EF%BC%9Af%281%29%2Cf%283%29%2Cf%28x%29%E7%9A%845%E9%98%B6%E5%AF%BC%E6%95%B0%E5%8F%8A8%E9%98%B6%E5%AF%BC%E6%95%B0%2C%E8%AF%B7%E9%97%AE%E5%90%84%E4%BD%8D%E5%90%8C%E4%BB%81%E6%80%8E%E4%B9%88%E6%B1%82%E5%95%8A%3F)
设函数f(x)=(x-1)(x-2)(x-3)(x-4)(x-5),求导:f(1),f(3),f(x)的5阶导数及8阶导数,请问各位同仁怎么求啊?
设函数f(x)=(x-1)(x-2)(x-3)(x-4)(x-5),求导:f(1),f(3),f(x)的5阶导数及8阶导数,请问各位同仁怎么求啊?
设函数f(x)=(x-1)(x-2)(x-3)(x-4)(x-5),求导:f(1),f(3),f(x)的5阶导数及8阶导数,请问各位同仁怎么求啊?
f(x)是一个五次多项式,因此其5阶导数只与最高次有关,结果为常数,所以f⁽⁵⁾(x)=5*4*3*2*1=120,为一个常数
则 f⁽⁵⁾(1)=f⁽⁵⁾(3)=f⁽⁵⁾(x)=120
则6阶以上导数全是0
f⁽⁸⁾(1)=f⁽⁸⁾(3)=f⁽⁸⁾(x)=0