二阶导数怎么求的,详细步骤

2025-01-02 02:20:50
推荐回答(1个)
回答1:

y=1+36x·(x+3)^(-2)

y'=36·(x+3)^(-2)+36x·[(x+3)^(-2)]'
=36·(x+3)^(-2)+36x·(-2)·(x+3)^(-3)
=36(3-x)·(x+3)^(-3)

y''=-36·(x+3)^(-3)+36x·[(x+3)^(-3)]
=-36·(x+3)^(-3)+36(3-x)·(-3)·(x+3)^(-4)
=36(x+3)^(-4)·[-(x+3)-3(3-x)]
=36(x+3)^(-4)·(2x-6)
=72(x+3)^(-4)·(x-3)