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已知函数f(x)=(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)求f‘(2) 导数问题
人气:207 ℃ 时间:2019-08-20 07:09:49
解答
f(x)=(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)
f'(x)=(x-1)'(x-2)(x-3)(x-4)(x-5)(x-6)+(x-1)(x-2)'(x-3)(x-4)(x-5)(x-6)+(x-1)(x-2)(x-3)'(x-4)(x-5)(x-6)+(x-1)(x-2)(x-3)(x-4)'(x-5)(x-6)+(x-1)(x-2)(x-3)(x-4)(x-5)'(x-6)+(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)'
=(x-2)(x-3)(x-4)(x-5)(x-6)+(x-1)(x-3)(x-4)(x-5)(x-6)+(x-1)(x-2)(x-4)(x-5)(x-6)+(x-1)(x-2)(x-3)(x-5)(x-6)+(x-1)(x-2)(x-3)(x-4)(x-6)+(x-1)(x-2)(x-3)(x-4)(x-5)
则除了第二项,其他都有x-2
所以x=2时等于0
所以f'(2)=(2-1)(2-3)(2-4)(2-5)(2-6)=24
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