设f(x)=(2x-1)(4x-1)(6x-1)(8x-1)(10x-1),求f '(1/2)如题 注意是求f(1/2)的导数

问题描述:

设f(x)=(2x-1)(4x-1)(6x-1)(8x-1)(10x-1),求f '(1/2)如题
注意是求f(1/2)的导数

这道题是多个乘积的复合函数的求导.设f(x)=g(x)*h(x)*k(x) 则f'(x)=g'(x)*h(x)k(x)+g(x)*[h(x)k(x)]' =g'(x)*h(x)k(x)+g(x)[h'(x)k(x)+h(x)k'(x)] = g'(x) h(x)k(x)+g(x) h'(x) k(x)+g(x)h(x) k'(x) 观察到三个乘积...